THE 


PRINCIPLES  OF   LOGIC 


HERBERT  AUSTIN  AIKINS,   PH.D. 

Leffingwell  Professor  of  Philosophy  in  the  College  for  Women  of 
Western  Reserve  University 


SECOND    EDITION,  REVISED 


NEW  YORK 
HENRY  HOLT  AND  COMPANY 


Copyright,  1902, 

BY 

HENRY  HOLT  &  CO. 


0% 


PREFACE  TO  THE   SECOND  EDITION. 

APART  from  the  Introduction  and  the  Conclusion  this  book  can  be 
divided  into  four  parts.  The  first  deals  with  the  interpretation  of 
language  and  the  blunders  that  result  from  a  disregard  of  its  exact 
meaning.  The  second  treats  of  deduction;  showing  what  inferences 
can  always  be  safely  drawn,  without  any  special  knowledge  of  the 
world,  from  one  or  two  supposedly  true  statements  of  a  given  type, 
and  what  can  not.  The  third  is  concerned  with  induction  in  the 
narrower  sense  of  the  term,  and  explains  the  methods  for  ascertaining 
or  testing  general  laws  of  nature  by  the  observation  of  particular 
facts  (thus  showing  how  we  can  justify  the  universal  propositions 
from  which  we  usually  reason  in  deduction).  The  fourth  shows  how 
these  general  laws  can  be  used,  in  turn,  for  the  discovery  of  new 
facts. 

Into  the  first  part  of  the  book  (Chapters  II-VII)  I  have  put  an 
extended  account  of  all  the  "semi-logical"  fallacies  and  of  certain 
others  which  depend,  like  them,  on  the  misuse  or  misunderstanding 
of  language.  To  understand  these  fallacies  requires  absolutely  no 
knowledge  of  logical  forms,  and  by  treating  of  them  at  the  outset 
we  do  away  with  an  unnecessary  barrier  between  the  deductive  part 
of  the  book  and  the  inductive,  arouse  the  student's  interest  at  the 
very  beginning,  and  make  him  less  likely  to  take  the  rigorous  accu- 
racy  that  is  necessary  in  syllogistic  reasoning  for  a  useless  quibbling 
and  mincing  of  words. 

One  cannot  go  far  in  the  interpretation  of  language  without 
coming  to  the  categories,  so  I  have  treated  of  them  here — briefly, 
and  I  hope  simply,  but  as  seriously  as  I  could. 

Chapter  IV  (on  Division  and  Classification)  does  not  really 
belong  to  the  first  part  of  the  book  at  all.  I  put  it  where  it  is  because 
of  its  intimate  relation  to  definition.  But  it  interrupts  the  continu- 


IV  PREFACE   TO   THE   SECOND   EDITION. 

ity  of  the  discussion,  and  it  would  have  been  better  to  put  the  first 
part  of  it  after  Chapter  IX  and  take  up  the  subject  of  classification 
in  connection  with  Chapters  XXX-XXXII. 

In  the  second  part  of  the  book  (Chapters  IV  and  VIII-XX)  I 
tred  to  treat  deduction  from  the  objective  or  realistic  standpoint,  as 
already  explained  in  the  preface  to  the  first  edition,  i.e.,  to  tell  how 
things  must  be  related  to  each  other  in  one  respect  if  they  are  also 
related  in  some  other  respect,  instead  of  talking  about  the  relations 
of  '  thoughts '  or  merely  giving  rules  for  the  arrangement  and 
manipulation  of  words;  and  I  tried  to  preserve  the  distinction 
between  the  different  categories,  instead  of  making  it  all  a  mere 
question  of  whether  one  class  does  or  does  not  include  a  part  of 
another.  This  involved  a  separate  treatment  for  each  of  the 
syllogistic  figures.  But  some  of  those  who  have  been  kind 
enough  to  criticise  the  book  think  that  a  shorter  treatment  along 
the  traditional  lines  would  have  been  sufficient  for  the  average 
student  and  have  left  him  with  something  more  available  for  instant 
use.  To  meet  their  views  I  am  adding  an  appendix  in  which 
syllogism  and  its  subsidiary  processes  are  treated  very  briefly  in  the 
ortho  'ox  way.  Those  who  are  pressed  for  time  and  are  content 
with  a  ready  rule  for  testing  arguments  can  use  this  appendix  as  a 
su'  stitute  for  Chapters  IV  and  VIII-XVI.  Others  also  might 
do  well  to  learn  the  appendix  first.  But  if  logic  is  to  serve  in  any 
way  as  an  introduction  to  metaphysics  the  text  should  not  be  omitted. 
For  we  cannot  ask  whethe  •  or  not  one  class  includes  part  of  another 
without  implying  the  possibility  of  an  answer  to  the  questions  there 
discussed  about  the  identity  and  qualities  of  things. 

In  the  chapter  on  the  Ill-conceived  Universe  I  hope  I  have  found 
an  appropriate  place  for  the  discussion  of  certain  material  fallacies 
that  it  is  customary  for  logicians  to  mention,  though  they  have  no 
special  relation  to  the  traditional  logical  doctrine,  and  for  certain 
others  not  usually  mentioned  at  all,  although  they  are  very  impor- 
tant. The  view  of  inference  that  I  took  throughout  the  whole  book 
enabled  me  to  give  them  a  very  definite  relation  to  its  pr  nciples. 

The  third  part  of  the  book  (Chapters  XXI-XXXII)  covers  the 
familiar  ground  of  induction,  with  chapters  on  Averages,  Probability, 
and  Statistics.  In  the  fourth  part  (Chapters  XXXIII-XXXV)  I 
have  worked  together  the  principles  of  historical  criticism  and  the 
legal  rules  of  evidence  to  cover  ground  not  always  included  in  text- 


PREFACE  TO   THE  SECOND   EDITION.  v 

books  of  logic.     And  in  the  Conclusion  I  have  inquired  into  the 
ultimate  justification  for  the  whole  logical  process. 

Some  reviewers  have  been  misled  by  my  use  of  the  borrowed 
term  "material" — I  said  "objective  or  'material'" — in  the  preface 
to  the  first  edition.  I  did  not  mean  to  say  that  my  standpoint  is 
materialistic,  for  it  is  not,  as  any  careful  reader  can  see;  but  only 
that  it  is  realistic  in  the  Scottish  sense— that  I  assume  the  existence 
of  something  more  than  homeless  'ideas'  or  'concepts',  and  make 
use  of  this  assumption  throughout — even  in  explaining  the  Law 
of  Contradiction. 

My  indebtedness  to  other  authors  is  apparent.  I  am  no  less 
indebted  to  individuals — particularly  to  colleagues  in  other  depart- 
ments who  have  given  me  valuable  suggestions  on  matters  related 
to  their  special  subjects;  but  most  of  all  to  Dr.  W.  T.  Marvin,  to 
whom  I  read  the  whole  book  while  it  was  still  in  manuscript. 

H.  A.  A. 

August,  1904. 


CONTENTS. 


CHAPTER  I.— INTRODUCTION. 

Two  kinds  of  thinking,  I — Judgments  and  propositions,  2 — A  dif- 
ferent view  of  judgments,  4 — Logical  thinking  is  objective,  6 — Scope 
of  logic,  6 — Truth  impersonal,  7 — Corollary,  9 — Fact  and  feel- 
ing, 10. 

CHAPTER   II.— THE  MEANINGS  OF  WORDS. 

Blunders  of  interpretation,  13 — How  words  become  ambiguous,  16 — 
What  ambiguities  are  most  dangerous,  17— Blunders  of  inference, 
22 — Paronymous  terms,  28 — How  to  deal  with  ambiguities,  29 — 
Definition^jp/- How  to  frame  definitions,  3 1— Illustrations,  32 — 
Where  precision  is  needed  most,  34. 

CHAPTER  III. — THE  MEANING  OF  STATEMENTS  AS  A 
WHOLE. 

Conventional  phrases,  36 — Oblique  senses,  37 — Exaggeration,  38 — 
Amphibology,  39 — Accident,  39 — Accent,  42. 

CHAPTER  IV. — DIVISION  AND  CLASSIFICATION. 

Relation  to  definition,  45 — Principles  of  division  and  subdivision,  45 — 
Cross-division.  47 — Some  technical  names,  50 — Scientific  classifica- 
tion and  its  purposes,  50 — Naming,  55. 

CHAPTER  V.— THE  USES  OF  SINGLE  WORDS  AND  PHRASES. 

Terms,  56 — Demonstrative  and  descriptive,  58  —  Connotative  and 
non-connotative,  60— Singular  and  general,  61 — Epithets,  62 — Col- 
lective and  distributive,  63 — The  danger,  64 — Abstract  and  con- 


Vin  CONTENTS. 

crete,  65 — Hypostatising  abstractions,  66 — Secondary  meaning  of 
'abstract',  70 — Positive  and  negative,  71 — Relative  and  absolute  : 
first  sense,  73 — Second  sense,  74 — Dangers,  75. 

CHAPTER  VI.— THE  RELATIONS    EXPRESSED  IN 
PROPOSITIONS. 

Five  fundamental  relations,  77 — Certain  combined  relations,  84. 

CHAPTER  VII. — WHAT    PROPOSITIONS  IMPLY  ABOUT 
EXISTENCE. 

The  two  '  subjects  ',  87 — Denials  of  relations  and  of  existence,  89 — 
The  conception  of  reality,  91. 

CHAPTER  VIII. — THE  FORMAL  CHARACTERISTICS  OF 
PROPOSITIONS. 

Quantity  and  quality,  96 — Ambiguities  of  quantity  and  quality,  98 — 
Undesignated  quantity  or  quality,  99 — Double  quantity,  102 — 
Exclusives  and  exceptives,  103  — Disjunctives  and  hypothetical,  106. 

CHAPTER  IX. — THE  OPPOSITION  OF  PROPOSITIONS. 

With  common  propositions,  in — With  exclusives  and  exceptives, 
115 — Symbols,  117. 

CHAPTER  X. — INFERENCE  AND   THE  SO-CALLED   LAWS  OF 
THOUGHT. 

Inference — what,  121  —  Deduction,  122— The  three  'Laws  of 
Thought',  124— Obversion,  130. 

CHAPTER    XI. — IMMEDIATE    INFERENCE,    OR    INFERENCE 
FROM  A  SINGLE  PREMISE. 

Conversion,  131 — The  traditional  treatment,  132 — The  treatment  by 
diagrams,  140 — A  broader  treatment,  142. 

CHAPTER  XII. — MEDIATE  INFERENCE  AND  SYLLOGISM. 

Limitations  of  deduction,  145 — 'Figures',  148. 


CONTENTS.  ix 

CHAPTER  XIII.  —  THE  FIRST  FIGURE  OF  THE  SYLLOGISM. 

General  function,  150 — Is  there  real  inference?  152 — Principle 
and  cautions,  155. 

CHAPTER^XJVi— THE  SECOND  FIGURE  OF  THE  SYLLOGISM. 

Function  and  general  cautions,  162 — Quantity  in  the  second  figure, 
167. 

CHAPTER  XV.— THE  THIRD  FIGURE  OF  THE  SYLLOGISM. 

Purpose,  principle,  and  general  caution,  171 — Negative  relations, 
174 — Quantity  of  the  premises,  175. 

CHAPTER  XVI.— THE  ALLEGED  FOURTH  FIGURE. 

Origin  of  the  figure,  176 — Three  ways  of  dealing  with  it,  176 — For- 
mal reduction,  178. 

CHAPTER  XVII.— OTHER  DEDUCTIVE  ARGUMENTS. 

Hypothetical  syllogisms,  183 — Disjunctive  syllogisms,  186 — Dilem- 
mas, 186 — Three  forms  of  abbreviated  argument,  188. 

CHAPTER  XVIII. — BLUNDERS    IN  WORD    AND  BLUNDERS 
IN  THOUGHT. 

'Purely  logical ',  193 — Two  kinds  of  material  fallacies,  195. 

CHAPTER  XIX.— THE  FORGOTTEN  ISSUE. 

Petitio  principii,  196 — Includes  epithets,  197 — And  circle,  197 — 
Ignoratio  Elenchi,  198  — Includes  'adhominem',  201. 

CHAPTER  XX.— THE  ILL-CONCEIVED  UNIVERSE. 

The  assumed  universe,  204 — The  confusion  of  universes,  208 — The 
neglected  aspect,  211 — The  neglected  member,  215 — The  neglected 
whole,  219. 

CHAPTER  XXI. — THE   DIFFERENCE   BETWEEN  INDUCTION 
AND  DEDUCTION. 

i    Difference  in  limitations,  221 — Difference  in  certainty,  226. 


x  CONTENTS. 

CHAPTER  XXII.— THE  UNIFORMITY  OF  NATURE. 

How  we  come  to  believe  in  it,  228 — Its  two  main  aspects,  232 — 
Law,  237 — Precision  in  uniformity,  238 — The  thing-aspect  of  this 
precision.  241 — Proof  of  uniformity,  243. 

CHAPTER  XXIII. — SCIENCE   AND    THE   PECULIARITIES  OF 
THE  RELATIONS  THAT  IT  TRACES. 

Twofold  work  of  science,  244 — Peculiarities  of  individual  identity 
and  causal  interaction,  245. 

CHAPTER  XXIV.— THE    METHOD    OF    EXHAUSTION  AND 
THE  SEARCH  FOR   PARTICULAR  UNIFORMITIES. 

4  Perfect  induction',  250 — Why  we  accept  less,  251 — Justification 
practical,  252 — When  may  we  guess?  252 — How  problems  and  re- 
lations are  interwoven,  253. 

CHAPTER  XXV. — INDUCTION    BY   SIMPLE    ENUMERATION 
AND  THE  SEARCH  FOR  CAUSES. 

Analysis,  inference,  and  explanation,  257 — -Analysis  and  clear 
thinking,  259. 

CHAPTER  XXVI.— THE    METHODS   OF  DIFFERENCE  AND 
AGREEMENT. 

Different  ways  of  exhausting  the  universe,  261 — The  method  of  dif- 
ference, 262 — The  method  of  agreement,  264 — Does  either  method 
really  exhaust?  265 — Advantages  of  each,  267 — Plurality  of  pos- 
sible causes,  267 — Two  kinds  of  data  compared.  270 — Post  hot  ergo 
fropter  hoc,  272 — Advantages  of  experiment,  272  — Assumption  in 
experiment,  273. 

CHAPTER  XXVII.— THE  JOINT    METHOD  OF  AGREEMENT 

AND  DIFFERENCE. 
Its  function,  275 — Compared  with  simple  method  of  difference.  278. 

CHAPTER  XXVIII. —COUNTERACTING  AND  COMPLEX 

CAUSES. 

Counteracting  causes,  281 — Causes  'compounded'  or  'combined', 
283. 


CONTENTS.  xi 

CHAPTER  XXIX. — THE  METHODS  OF  RESIDUES  AND 
CONCOMITANT  VARIATIONS. 

Quantitative  treatment  of  causes,  287  — Method  of  residues,  288 — 
Method  of  concomitant  variations,  290 — Cautions,  293. 

CHAPTER  XXX. — GROUP  COMPARISONS,  OR  THE  METHOD 
OF  STATISTICS. 

Principle  and  uses,  296 — Numl>er  of  data,  300 — Personal  equation, 
etc..  300— Preconceptions  and  interests,  302 — Accidental  selection, 
304 — Misplaced  accuracy,  306. 

CHAPTER  XXXI.— MEANS,  OR  AVERAGES. 

General  conception.  312 — Various  kinds,  313 — First  use  of  average, 
317 — Second  use  of  average,  320 — Third  use  of  average,  324 — 
Measures  of  error,  327. 

CHAPTER  XXXII.— PROBABILITY. 

Why  needed.  330 — What  it  is  not,  331 — What  it  is,  333 — What 
value?  334 — Why  hard  to  estimate,  336 — Caution,  337 — Mathe- 
matical principles,  338 — Four  more  cautions.  340. 

CHAPTER  XXXIII.— OBSERVATION  AND  MEMORY. 

Observation  and  inference,  343  —  Credulity,  345 — Errors  cumulative, 
347 — Unprejudiced  observers,  347 — Two  classes  of  errors.  348 — 
Memory  and  its  dangers,  350 — What  we  remember,  350  —  Honest 
lies,  352 — Resulting  commonplaces,  354. 

CHAPTER  XXXIV.— THE  DISCOVERY  OF  PAST  AND 
FUTURE  EVENTS  IN  GENERAL. 

The  starting-point.  357— The  limit,  358 — '  Monuments  ',  359 — Cir- 
cumstantial evidence,  361. 

CHAPTER  XXXV.— TESTIMONY. 

Its  importance,  363 — Its  unique  value  and  danger,  364 — Accepting,, 
rejecting,  and  weighing,  364— Expert  evidence  ;  caution.  367— In- 
ferring without  trusting,  371  —  More  refined  methods,  373 — Who  is 


xii  CONTENTS. 

the  witness  ?  376 — Joint  authorship,  378 — How  does  he  know  ?  384 
• — Hearsay,  384 — Is  he  truthful  ?  386 — Arbitrary  tests,  386 — 
Character,  387  — Circumstances,  388 — Interests,  389 — Consistency 
and  general  probability,  392 — Confirmation  and  contradiction, 
393 — The  judge  must  judge  impartially,  397 — According  to  evi- 
dence, 398 — Must  judge  for  himself,  398 — Must  have  a  problem  and 
make  it  definite,  400— Issue  before  evidence,  402 — Must  not  be 
managed  by  the  witnesses,  403 — Must  not  decide  in  a  hurry,  404. 

CHAPTER  XXXVI.— THE  THREE    ULTIMATE  TESTS  OF 
TRUTH. 

Consistency,  405 — Conceivability,  406 — The  third  test,  409 — Uni- 
formity in  the  mass,  409 — Analogy,  413 — Absurdity,  414 — Sim- 
plicity, 416 — The  right  to  assume  these  principles,  421 — The 
limits  of  proof,  423. 

EXERCISES , 427 

APPENDIX 485 

INDEX 495 


LOGIC. 

CHAPTER    I. 
INTRODUCTION. 

THE  business  of  Logic  is  to  help  us  to  think  clearly  and 
objectively,  express  ourselves  plainly  and  accurately,  reason 
correctly,  and  estimate  aright  the  statements  and  arguments 
of  others. 

We  cannot  fully  understand  what  is  meant  by  the  state- 
ment that  logic  helps  us  to  think  clearly  unless  we  dis- 
tinguish carefully  between  two  kinds  of  thinking. 

The    first    kind   makes   some   statement  or  asks   J,?r0j£ind8  of 

tnin&iiig . 

some  question ;  the  second  consists  in  a  mere 
play  of  mental  images,  such  as  takes  place  when  we  follow 
quite  passively  the  successive  notes  of  a  piece  of  music, 
hearing  each  as  it  passes  but  doing  nothing  more,  or  when 
the  music  runs  through  our  head  afterwards  in  the  same 
way,  or  when  half-dozing  we  watch  the  pictures  that  float 
before  us,  or  when  in  the  same  passive  way  we  feel  yet  do 
not  note  the  sensations  that  come  from  our  limbs  as  we 
walk  or  row  or  take  some  other  such  mechanical  exercise. 
But  just  as  soon  as  we  recognize  that  the  music  is  or  is  not 
beautiful,  that  one  note  is  following  another,  that  some  one 
is  playing,  or  that  we  are  hearing,  feeling,  or  imagining 
something,  then  we  get  back  for  the  moment  at  least  to 
the  first  kind  of  thinking;  for  to  the  mere  passive  images 


2  INTRODUCTION. 

we  have  added  something  else  and  there  is  now  an  active 
affirmation  or  denial. 

The  second  kind  of  thinking — that  which  consists  in  the 
mere  play  of  sensations  or  images — serves  no  purpose  beyond 
the  pleasure  or  recreation  of  the  thinker;  and  logic  has 
nothing  to  do  with  it.  Consequently,  when  we  speak  of 
clear  thinking  we  do  not  refer  to  the  vividness  or  continuity 
of  such  passive  images,  but  rather  to  the  definiteness  and 
consistency  of  active  affirmations,  denials,  or  questions. 

When  we  affirm  or  deny  anything  we  are  said  to  form  a 
belief,  to  come  to  a  conclusion,  or  to  pass  a  judgment;  and 

the  sentence  in  which  the  judgment  is  expressed 
Judgments 

and  propo-  is  called  a  proposition.  Propositions  can  thus 
aitions.  .  .  , 

be   denned   as  sentences   expressing  judgments. 

According  to  this  definition  interrogative  sentences  are  not 
propositions,  for  a  question  implies  the  absence  of  a  judg- 
ment. On  the  other  hand  negative  sentences  are  proposi- 
tions; for  it  is  quite  as  much  an  act  of  judging  to  deny  that 
something  is  the  case,  e.g.,  to  say  or  think  '  The  day  is  not 
hot',  as  to  affirm  it — to  say  or  think  'The  day  is  hot'. 
There  is  thus  a  vast  difference  between  saying  that  a  thing 
is  not  so  and  not  saying  that  it  is  so,  in  spite  of  the  fact  that 
we  often  say  '  I  do  not  think  so  '  when  we  mean  '  I  think 
not  '. 

Judgments  always  have  reference  to  something  other  than 
themselves.  Like  the  eye  which  always  looks  outward  and 
never  sees  itself,  they  are  always  concerned  with  some  object 
or  other  which  lies  beyond  them,  and  never  with  themselves. 
This  is  most  important.  Perhaps  it  can  be  made  clear  by 
an  illustration  from  grammar.  When  I  say  *-'  The  word 
'  good  '  is  an  adjective  ",  I  am  speaking  of  that  word  as  it 
occurred  somewhere  else;  for  as  I  use  it  here  it  is  a  noun. 
Words  never  refer  to  themselves,  but  to  something  else 
which  they  name  or  '  mean  '.  The  same  is  true  of  judg- 
ments. When  I  say  "  The  house  is  on  fire  ",  I  do  not  mean 
to  state  anything  about  myself  or  about  my  judgment  with 


JUDGMENTS   AND   PROPOSITIONS.  3 

reference  to  the  house.  I  do  not  even  mean  to  say  that  I 
judge  that  the  house  is  on  fire.  I  do  judge  it;  and  the 
statement  expresses  my  judgment.  But  to  express  a  judg- 
ment is  to  tell  something  about  the  object  thought  about  or 
judged  of — in  this  case  the  house — not  about  the  thought 
or  judgment  itself,  or  the  person  who  passes  it,  or  the  words 
in  which  it  is  expressed.  When  we  wish  to  see  our  own 
eyes  we  do  not  look  at  them  directly,  but  at  their  image  in  a 
mirror.  So  when  we  wish  to  know  our  own  thought  we 
must  get  a  new  thought  with  the  thought  in  question  as  its 
object,  e.g.,  ' I  thought  that  the  house  was  on  fire',  or 
'  I  recognized  that  the  house  was  on  fire  '.  In  these  proposi- 
tions I  am  talking  about  my  own  thought  or  judgment;  in 
the  former  I  was  not.  But  even  here  the  thought  of  which 
I  am  speaking  is  not  the  thought  that  I  am  expressing,  for 
I  am  speaking  of  the  past  thought  and  expressing  the  present 
thought  about  it. 

That  about  which  a  judgment  is  passed,  i.e.,  that  about 
which  something  is  asserted  (affirmed  or  denied),  is  called 
the  Subject  or  Object  of  our  thought.  If  it  is  a  real  thing  or 
person,  it  is  also  called  the  subject  of  the  relations  that  are 
affirmed  of  it,  and  the  word  used  to  point  it  out  is  usually 
the  subject  of  the  sentence  or  proposition  in  which  the  judg- 
ment is  expressed.  Thus,  in  the  example  just  given,  the 
real  house  is  the  subject  of  the  state  we  call  being  on  fire, 
for  it  is  the  house- — not  something  else — that  is  blazing;  the 
real  house  is  the  subject  of  the  judgment,  for  it  is  the  real 
house  that  I  am  thinking  and  speaking  about;  but  it  is  the 
word  '  house  '  that  is  the  subject  of  the  sentence.  It  is  not 
the  word  '  house  '  that  is  on  fire  or  of  which  I  am  thinking 
or  speaking,  and  it  is  not  the  real  house  that  is  part  of  a 
sentence.  Thus  the  subject  of  a  sentence  is  not  that  about 
which  something  is  stated  in  the  sentence,  but  it  is  the  name 
0/"that  about  which  something  is  stated. 

We  should  never  confuse  these  three  different  meanings 
of  the  word  Subject — what  we  are  thinking  about,  or  the 


4  INTRODUCTION. 

subject  of  thought;  the  thing  that  is  in  a  certain  state,  or 
the  subject  of  that  state;  and  the  name  of  what  we  are 
thinking  and  speaking  about,  or  the  subject  of  a  sentence. 

There  are  plenty  of  logicians  and  other  writers  who  have 
not  made  or  recognized  this  distinction.      Locke,  for  exam- 
ple,   who  wrote  more  than  two  hundred   vears 
A  different 
view  of          ago,  tells  us  in  his  celebrated      Essay  Concerning 

Human  Understanding  "  that  knowledge  is  "  the 
perception  of  the  agreement  or  disagreement  of  our  ideas  ". 
This  definition  takes  no  account  whatever  of  the  things 
beyond  our  ideas  to  which  they  are  supposed  to  refer.  So 
Jevons  tells  us  in  his  "  Lessons  in  Logic  ",  a  text-book  that 
is  very  widely  used,  that  an  act  of  judgment  "  consists  in 
comparing  together  two  notions  or  ideas  of  objects  derived 
from  simple  apprehension,  so  as  to  ascertain  whether  they 
agree  or  differ".  But  when  we  judge  that  the  house  is  on 
fire  we  do  not  compare  our  idea  of  the  house  with  our  idea 
of  fire,  find  that  in  some  way  or  other  the  two  ideas  '  agree  ', 
and  then  use  the  copula  '  is  '  to  indicate  the  agreement  and 
to  fasten  the  two  agreeing  ideas  together.  On  the  contrary 
we  are  usually  wholly  absorbed  in  the  house  and  its  fate  and 
do  not  think  about  our  own  ideas  at  all.  When  we  say  that 
a  person  can  tell  '  only  about  his  own  ideas  of  things  '  it 
would  be  more  accurate  to  say  that  he  can  express  only  his 
own  opinions.  But  to  express  an  opinion  about  a  thing 
is  to  tell  not  about  the  opinion  itself — about  one's  own 
thoughts  and  their  relations  to  each  other — but  about  the 
thing  as  one  believes  it  to  be,  its  states  and  its  relations  to 
other  things.  If  we  really  agreed  with  Locke  when  he  says 
or  implies  that  everything  we  know  is  our  own  idea  instead 
of  something  beyond  it,  we  should  have  to  agree  also  with 
Hume  when  he  says  that  we  "  can  form  ideas  which  shall  be 
no  greater  [i.e.,  larger]  than  the  smallest  atom  of  the  animal 
spirits  of  an  insect  or  a  thousand  times  less  than  a  mite", 
merely  because  we  can  think  of  things  so  small;  when  he 
speaks  of  perceptions  or  sensations  as  "  composed  of  parts  " 


A   DIFFERENT   VIEW  OF  JUDGMENTS.  5 

because  the  things  that  we  perceive  or  feel  are  so  composed; 
ami  when  he  seriously  discusses  "  the  infinite  divisibility  of 
our  ideas  of  space  and  time.  "  * 

If  there  is  no  distinction  between  thought  and  the  object 
thought  of,  Hume  is  right  enough  in  talking  of  large  and 
small  iJcas;  but  if  there  is  a  distinction,  we  must  not  assume 
that  a  thought  of  a  large  or  complex  object  is  any  larger  than 
the  thought  of  one  that  is  small  or  simple.  A  good  photo- 
graph of  a  single  brick  involves  just  as  complex  a  chemical 
process  on  the  sensitive  plate  as  that  of  a  whole  house;  to 
pick  a  single  grape  is  just  as  complex  an  act  as  to  pick  a 
whole  bunch ;  and  in  the  same  way  to  think  of  a  mob  is  not 
to  have  a  mob  of  thoughts.  Some  acts  of  thinking  are  un- 
doubtedly more  complex  than  others;  but  the  complexity 
of  the  thought  in  no  way  corresponds  with  that  of  the  object 
thought  about,  f 

*  See  his  "  Treatise  of  Human  Nature  ",  Book  I,  Part  II,  Sec.  I.  i 
David  Hume  lived  from  1711  to  1776.  He  was  probably  the  greatest  of  ' 
all  British  philosophers. 

•j-  As  for  the  '  simple  apprehension  '  spoken  of  by  Jevons  and  so  many 
other  writers,  it  has  little  or  nothing  to  do  with  an  act  of  judgment.  \Ve 
can  divide  a  sentence  into  subject  and  predicate,  or,  if  we  like,  into 
subject,  predicate,  and  copula  ;  but  we  cannot  make  any  such  division 
in  the  judgment  which  the  sentence  expresses.  "  Simple  apprehension  ", 
says  Jevons,  "  is  the  act  of  mind  by  which  we  merely  become  aware  of 
something,  or  have  a  notion,  idea,  or  impression  of  it  brought  into  the 
rnind.  The  adjective  simple  means  apart  from  other  things,  and  appre- 
hension the  taking  hold  by  the  mind.  Thus  the  name  or  term  Iron  in- 
stantaneously makes  the  mind  think  of  a  strong  and  very  useful  metal, 
but  does  not  tell  us  anything  about  it,  or  compare  it  with  anything  else." 
{Elementary  Lessons  in  Logic,  p.  II.)  But  let  the  reader  spend  five  min- 
utes trying  to  think  of  such  a  metal  without  making  some  statement 
about  it.  He  can  say  '  Iron  is  strong,'  or  '  Iron  is  useful,'  or  '  Iron  is 
a  metal,'  or  'This  is  iron,'  and  during  the  five  minutes  he  will  doubt- 
less make  an  immense  number  of  other  statements;  but  when  he  tries  to 
think  of  it  without  discovering  some  relation  or  passing  some  judgment 
he  will  probably  find  himself  mechanically  repeating  some  word  appli- 
cable to  iron  and  really  thinking  about  something  else;  or  it  may  be 
that  with  the  word  upon  his  lips  or  some  visual  image  in  his  phantasy 


6  INTRODUCTION. 

Since  all  thinking  has  reference  to  some  reality  beyond 
itself,  we  think  clearly  when  we  discern  the  object  that  we 

are   thinking  about  without  confusion,   and  we 
Logical 
thinking  is     reason  correctly  when  we  see  how  one  relation 

of  a  thing  involves  another.  In  order  to  think 
clearly  and  reason  correctly  it  is  therefore  necessary  to  look 
outwards  continually  beyond  ourselves  and  beyond  the  words 
used  by  others  towards  the  things  that  we  or  they  are  think- 
ing about,  in  order  to  see  these  things  and  all  their  essential 
relations  as  they  are.  Unless  we  do  this  we  cannot  succeed 
either  in  expressing  ourselves  plainly  and  accurately  or  in 
forming  a  right  estimate  of  the  reasoning  of  others.  Thus 
the  habit  of  closely  examining  the  reality  beyond  us  and  of 
testing  all  our  thoughts  and  words  with  reference  to  that 
reality  is  necessary  for  all  the  aims  of  logic. 

Logic  is  often  denned  as  the  science  of  the  laws  of 
thought;  but  if  what  we  have  been  saying  is  correct,  it  would 
Scope  of  be  far  more  appropriate  to  say  that  it  points  out 
the  laws  of  things  which  all  thought  should 
respect,  or  that  it  deals  with  the  mutual  implications  of  the 
relations  of  things.  The  special  sciences  and  metaphysics 
also  study  relations  of  things  and  the  way  in  which  one 
involves  another,  but  with  a  somewhat  different  purpose. 
Each  of  the  special  sciences  is  concerned  with  some  one 
group  of  things  and  relations,  and  when  it  inquires  how  one 
relation  involves  another  it  is  for  the  sake  of  gaining  more 
knowledge  about  the  particular  things  and  relations  in  ques- 
tion. Its  aim  is  thus  the  attainment  of  wider  or  more  exact 
knowledge  in  some  one  special  field.  Metaphysics,  on  the 
other  hand,  inquires  into  the  most  fundamental  and  general 
relations  of  all  things,  and  tries  to  find  out  what  the  inmost 
nature  of  any  thing  must  be  in  order  that  all  of  these  rela- 
tions should  belong  to  it  together.  Logic,  like  metaphysics, 

lie  will  find  consciousness  itself  flickering  and  disappearing. — If  simple 
apprehensions  exist,  they  form  no  part  of  our  knowledge,  of  our  coherent 
thought,  or  of  our  reasoning.  All  these  involve  judgments. 


TRUTH   IMPERSONAL.  7 

has  a  very  general  aim ;  it  too  inquires  into  the  most  funda- 
mental relations  of  things  and  the  way  in  which  one  in- 
volves another.  But  its  inquiry  is  not  so  profound  as  that 
of  metaphysics;  it  does  not  ask  what  the  inmost  nature  of 
things  must  be  in  order  that  these  relations  should  exist 
together  in  them;  and  the  knowledge  that  it  does  try  to 
gain  about  relations  and  their  mutual  implications  it  regards 
as  a  means,  not  as  an  end.  We  cannot  reason  at  all  in  sci- 
ence or  anything  else  unless  we  have  some  idea  of  them,  and 
we  cannot  reason  correctly  unless  our  idea  of  them  is  essen- 
tially correct;  but  it  may  be  correct  enough  to  enable  us  to 
reason  well  about  most  subjects  without  being  nearly  so 
profound  as  advanced  metaphysical  inquiries  try  to  make  it. 
Thus  in  so  far  as  logic  tries  to  make  us  reason  correctly  by 
giving  us  correct  conceptions  of  things  and  the  way  in  which 
their  relations  involve  each  other,  it  is  a  kind  of  simple  meta- 
physics studied  for  a  practical  end. 

There  is  a  sense,  however,  in  which  it  is  perfectly  true  that 
logic  deals  with  '  laws  of  thought '.  A  law  of  thought  tells 
how  people  actually  do  think,  just  as  a  law  of  astronomy 
tells  how  heavenly  bodies  actually  move,  and  the  real  science 
of  the  laws  of  thought  is  therefore  psychology;  but  inasmuch 
as  there  are  certain  natural  ways  of  thinking  that  lead  to 
various  kinds  of  logical  blunders,  it  is  necessary  to  understand 
them  in  order  to  understand  why  we  make  the  blunders. 
Thus  in  so  far  as  logic  deals  with  various  kinds  of  fallacies 
which  we  naturally  commit  and  tries  to  explain  their  origin, 
it  is  touching  on  the  field  of  psychology  and  dealing  with 
'  laws  of  thought '. 

Every  judgment,   true  or  false,   asserts  something   about 
some   supposed    reality    beyond    itself,    and    the    difference 
between  the  true  and  the  false  is  that  the  state  of  Truth  im- 
affairs  asserted   by  the  former  really  exists  and   P6™011*1' 
that   asserted  by  the  latter  does  not.     Whether  it  does  or 
does  not  depends  altogether  upon  the  nature  of  things  and 
the  presence  or  absence  of  the  conditions  that  might  naturally 


8  INTRODUCTION. 

produce  it.  It  does  not  depend  at  all  upon  the  judgment 
about  it.  Whether  the  sun  is  shining  or  not  at  a  certain 
place  depends  altogether  upon  the  time  of  day  and  the  pres- 
ence or  absence  of  clouds,  fog,  and  an  eclipse.  If  such 
conditions  as  these  are  all  favorable,  the  sun  is  certainly 
shining  whether  I  happen  to  think  so  or  not;  and  if  I  say  it 
is  not  shining  when  it  really  is,  my  statement  is  false  no 
matter  who  I  am  or  how  sincere  I  may  be  in  making  it;  so 
likewise  if  I  have  nervous  prostration  or  a  broken  leg,  I  have 
it  no  matter  who  says  that  I  have  or  that  I  have  not. 
Hence  it  is  arrant  nonsense  to  say  that  something  may  be 
'true  for  one  person  and  false  for  another'.  One  person 
may  believe  that  a  statement  is  true  and  another  may  believe 
that  it  is  not,  but  the  facts  are  what  they  are  wholly  regard- 
less of  these  conflicting  beliefs,  and  one  of  the  persons  must 
be  wrong.  If  every  possible  statement  could  really  be  true 
for  one  person  and  false  for  another,  then  every  one  would 
always  be  right  in  what  he  thought  no  matter  what  it  was, 
and  there  would  be  no  such  thing  as  an  error  or  mistake, 
and  therefore  no  distinction  between  correct  thinking  and  in- 
correct. All  logic  is  based  on  the  assumption  that  there  is 
such  a  distinction,  and  therefore  from  the  standpoint  of  logic 
no  blunder  could  be  more  fundamental  or  destructive  than 
that  which  is  involved  in  the  serious  belief  that  something 
may  be  '  true  for  one  person  and  false  for  another '. 

The  notion  that  some  fact  might  exist  '  for '  one  person 
and  not  '  for  '  another  doubtless  arises  from  the  existence  of 
individual  differences  in  matters  of  taste  and  a  certain  con- 
fusion about  their  meaning.  If  a  picture  pleases  me,  I  say 
it  is  beautiful ;  and  if  it  displeases  you,  you  say  it  is  ugly ;  and 
all  that  either  of  us  has  any  right  to  mean  by  the  statement 
is  that  the  picture  does  please  him  or  displease  him.  Each 
statement  thus  tells  about  the  relation  between  two  things, 
the  picture  and  the  beholder;  and  because  of  the  difference 
between  the  two  beholders  both  statements  understood  in 
this  way  may  be  perfectly  true;  the  picture  really  is  beautiful 


COROLLARY.  9 

for  me  and  really  is  ugly  for  you,  and  there  is  nothing  more 
to  be  said — de  gustibus  nil  disputandum.  But  these  words 
'  beautiful  '  and  '  ugly  '  and  others  like  them  have  the  same 
grammatical  form  as  words  like  '  square '  and  '  round  ' 
which  really  tell  about  the  thing  itself,  quite  regardless  of  its 
relations  to  the  beholder;  and  this  helps  to  make  us  ignore 
the  difference  between  them  and  assume  that  somehow  or 
other  we  can  describe  the  thing  itself  (as  we  do  with  such 
words  as  '  round  '  and  '  square  '),  while  at  the  same  time  the 
truth  of  the  description  depends  (as  it  does  with  such  words 
as  '  beautiful  '  and  '  ugly  ')  upon  who  it  is  that  gives  it. 

Somewhat  like  the  statement  that  something  may  be  true 
for  one  person  and  false  for  another  is  the  statement  that  it 
may  be  true  in  one  science  and  false  in  another.  Towards 
the  end  of  the  middle  ages  the  monkish  philosophers  found 
themselves  reaching  conclusions  that  were  quite  contrary  to 
the  doctrine  of  the  Church  which  they  were  bound  to  accept. 
So  they  said  that  there  was  a  difference  between  theology 
and  philosophy,  that  a  doctrine  might  be  true  in  one  though 
false  in  the  other,  and  that  they  accepted  all  the  teachings 
of  the  Church  as  true  in  theology,  though  they  might  reject 
a  part  of  them  as  false  in  philosophy.  By  this  subterfuge 
they  tried  to  give  an  excuse  for  continuing  their  thinking  as 
freely  as  possible  and  yet  save  their  heads  by  remaining  in 
nominal  subservience  to  the  Church.  Of  course  this  doctrine 
of  a  '  double  truth  '  was  nothing  but  a  subterfuge,  and  it  dis- 
appeared when  men  gained  the  right  to  exercise  their  own 
individual  judgment  in  matters  of  belief. 

Since  the  reality  with  which  all  thought  is  concerned  is 
something  different  from  the  thought  itself,  we  have  no  right 

to   assume  without    evidence  that   there  is  any 

.  .     .         Corollary, 

relation  between  them  beyond  the  bare  relation 

of  knower  and  object  known.  We  have  no  right  to  assume 
that  our  thoughts  are  like  things — e.g.,  that  our  thought  of 
the  moon  is  round  like  the  moon  itself — or  that  they  have 
the  same  history  or  are  subject  to  the  same  laws.  We  have 


io  INTRODUCTION. 

no  right  to  assume,  for  example,  that  distant  events  are  any 
more  vague  than  those  of  the  present  simply  because  our 
ideas  of  them  are  more  vague,  or  that  things  were  vague  and 
chaotic  before  they  were  definite  because  our  ideas  of  them 
were. 

Facts  are  as  independent  of  our  feelings  as  they  are  of  our 
ideas.      Hence  when  we  are  trying  to  find  out  what  the  facts 
Fact  and         really    are   we    must    not    ask    instead  what  we 
eiing.  should  like  them  to  be  and  assume  that  we  have 

answered  the  first  question  when  we  have  only  answered  the 
second.  Yet  obvious  as  this  is,  the  tendency  to  confuse  the 
facts  as  they  are  with  what  we  should  like  them  to  be  is 
exceedingly  strong.  Indeed  it  is  so  strong  that  hardlv  any 
one  can  overcome  it  altogether.  To  do  so — to  look  facts 
squarely  in  the  face  and  accept  them  as  they  are,  no  matter 
how  pleasant  or  unpleasant  they  may  be — is  one  of  the  very 
first  conditions  of  greatness,  and  it  is  always  a  mighty  aid  to 
success  in  any  career.  Moreover  it  is  something  which  does 
not  require  any  unusual  mental  ability.  But  it  does  require 
intellectual  honesty;  and  because  very  few  of  us  arc  willing 
to  be  absolutely  honest  in  our  thought  those  who  are  so 
often  seem  heroic.  Thj  'Appeal  t<>  Consequences' ',  on  the 
other  hind — the  argument  which  really  invites  one  to  accept 
a  certain  view  merely  because  the  view  itself  or  something 
else  that  it  involves  is  more  pleasant  to  believe  in  than  the 
contrary — is  thoroughly  contemptible,  and  yet  it  is  some- 
thing to  which  we  are  so  accustomed  that  it  takes  a  strong 
man  with  a  great  love  for  truth  to  show  us  how  contemptible 
it  really  is.  I  quote  the  following  from  the  account  of  the 
discussion  of  evolution  at  the  Oxford  meeting  of  the  British 
Association  in  1860  in  the  Life  of  Professor  Huxley 
(vol.  i.  pp.  197-8):  "The  Bishop  spoke  thus  '  for  full  half 
an  hour  with  inimitable  spirit,  emptiness,  and  unfairness.' 
'  In  a  light,  scoffing  tone,  florid  and  fluent,  he  assured  us 
there  was  nothing  in  the  idea  of  evolution  ;  rock-pigeons  were 
what  rock-pigeons  had  always  been.'  '  Then  "  he  rhetori- 


FACT   AND   FEELING.  II 

cally  invoked  the  aid  of  feeling,  and  said,  '  If  any  one  were 
willing  to  trace  his  descent  through  an  ape  as  his  grand- 
father, would  he  be  willing  to  trace  his  descent  similarly  on 
the  side  of  his  grandmother  r> '  '  "On  this  Mr.  Huxley 
slowly  and  deliberately  arose.  A  slight  tall  figure,  stern  and 
pale,  very  quiet  and  very  grave,  he  stood  before  us  and  spoke 
those  tremendous  words — words  which  no  one  seems  sure 
of  now,  nor,  I  think,  could  remember  just  after  they  were 
spoken,  for  their  meaning  took  away  our  breath,  though  it 
left  us  in  no  doubt  as  to  what  it  was.  He  was  not  ashamed 
to  have  a  monkey  for  his  ancestor;  but  he  would  be  ashamed 
to  be  connected  with  a  man  who  used  great  gifts  to  obscure 
the  truth.  No  one  doubted  his  meaning,  and  the  effect  was 
tremendous.  One  lady  fainted  and  had  to  be  carried  out; 
I,  for  one,  jumped  out  of  my  seat." 

No  one  can  think  clearly  and  reason  correctly  or  be  relied 
upon  by  others  as  fair-minded  and  impartial  who  believes  that 
any  view  of  things  is  right  if  it  is  not  true,  or  who  does  not 
strive  with  all  his  might  to  see  things  as  they  really  are  in 
spite  of  all  his  wishes. 

Our  feelings  tend  to  influence  our  judgment  not  only  by 
making  us  believe  what  it  is  pleasant  to  believe,  but  also  by 
making  us  believe  whatever  happens  to  fit  in  with  the 
emotion  of  the  moment.  Leslie  Stephen  says:  '  We  are  not 
unhappy  because  we  believe  in  hell;  but  we  believe  in  hell 
because  we  are  unhappy.'  When  we  are  despondent  the 
world  seems  dark  and  sad,  when  we  are  happy  it  seems 
bright  and  glad,  when  we  are  in  love  it  is  easy  to  find 
"  Helen's  beauty  in  a  brow  of  Egypt",  and  when  we  are 
angry  or  irritated  it  is  hard  to  believe  that  anger  or  irritation 
is  out  of  place. 

"  Speak  roughly  to  your  little  boy, 
And  beat  him  when  he  sneezes. 
He  only  does  it  to  annoy, 

Becauses  he  knows  it  teases." 

This  certainly  is  the  logic  of  the  emotions,  and  it  is  hard 


12  .        INTRODUCTION. 

enough  to  overcome  it — until  the  mood  is  over;  and  if  we 
must  wait  until  then  to  see  things  as  they  are,  we  should  also 
make  it  a  rule  to  wait  before  we  express  or  act  upon  our 
judgments.  Hence  the  wisdom  of  counting  one  hundred 
before  displaying  anger,  and  of  the  regulation  which  obtains, 
I  believe,  in  the  British  navy  requiring  that  no  officer  shall 
punish  a  man  until  twenty-four  hours  after  the  supposed 
offence. 

In  our  effort  to  see  things  as  they  are  in  spite  of  our 
wishes  and  emotions  we  often  have  to  resist  an  appeal  to 
them  made  wittingly  or  unwittingly  by  some  one  else. 
When  any  one  discusses  the  question  at  issue  on  its  own 
intrinsic  merits  he  is  said  to  reason  to  the  point,  or,  as  the  old 
logicians  would  say,  his  is  an  Argumentum  ad  Rem;  but  when 
one  party  to  a  discussion  takes  advantage  of  the  weakness  of 
another  and  tries  to  persuade  him  that  something  is  true  by 
appealing  to  his  wishes  or  his  emotions  he  uses  one  form  of 
the  Argumentum  ad  Hominem.  Since  the  essential  purpose 
of  this  so-called  argument  is  to  leave  a  person  in  a  certain 
mood  which  will  affect  his  judgment,  it  makes  very  little 
difference  how  it  is  done.  It  may  be  by  gentle  or  inflamma- 
tory speeches  or  it  may  be  without  speech  at  all — by  feeding 
him  or  embarrassing  him  or  getting  him  out  in  the  moon- 
light. 

The  Argumentum  ad  Populum  is  essentially  the  same  as  this 
form  of  the  Argumentum  ad  Hominem  except  that  it  is 
addressed  to  a  crowd.  The  real  arguments  of  successful 
political  speakers  are  generally  very  weak.  They  carry  their 
point  and  get  the  votes  merely  by  gaining  the  sympathy  of 
the  audience:  by  getting  it  to  fjel  in  harmony  with  the 
speaker  and  out  of  harmony  with  his  opponents;  and  it  does 
not  make  much  difference  whether  this  is  done  by  solid 
arguments,  impassioned  appeals,  ridicule  and  abuse  of  the 
other  side,  or  funny  stories. 


CHAPTER   II. 
THE   MEANINGS   OF   WORDS. 

IN  almost  all  our  thought  and  our  communication  with 
others  we  use  words.  A  word  is  "  a  mark  which  may  raise 
in  our  mind  a.  thought  like  to  some  thought  which  we  had 
before,  and  which,  being  pronounced  to  others,  may  be  to 
them  a  sign  of  what  thought  the  speaker  had  before  in  his 
mind".  Unfortunately,  however,  the  thing  or  the  relation 
which  a  given  word  is  used  to  mark  is  not  always  the  same, 
and  if  we  assume  that  it  is  in  any  particular  case  when  in 
fact  it  is  not,  we  are  bound  to  misunderstand  each  other,  to 
make  some  egregious  blunder  in  our  own  reasoning,  or  not 
to  notice  such  blunders  in  the  reasoning  of  others. 

To  speak  first  of  the  blunders  of  interpretation.  These 
often  arise  when  a  student  is  beginning  the  study  of  any 

science  and  takes  it  for  granted  that  words  which 

,     .     .  .       Blunders  of 

are  used  in  a  purely  technical  sense  are  used  in   interpreta- 

the  popular  sense  to  which  he  happens  to  be 
accustomed.  The  word  '  phenomenon  '  as  used  in  science 
merely  means  something  that  we  perceive  or  appear  to  per- 
ceive, but  the  student  assumes  that  it  means  something 
strange  or  miraculous.  When  the  psychologist  speaks  of 
'  imagining  '  something  he  merely  means  forming  a  mental 
picture  of  it;  but  the  student  may  assume  that  he  means 
believing  something  that  is  not  so.  '  Immediate  '  in  science 
means  direct  or  without  the  assistance  of  anything  else;  but 
the  student  will  probably  assume  that  it  means  without  any 

13 


14  THE   MEANINGS   OF   WORDS. 

delay.  A  '  particular '  proposition  in  logic  is  one  that  tells 
about  some  undesignated  part  (cf.  'particle')  of  a  class; 
but  the  student  who  reads  his  book  in  a  hurry  assumes  that 
it  is  one  that  tells  about  some  individual  in  particular. 
When  a  student  misinterprets  statements  in  this  way  he  is 
almost  certain  to  misconceive  the  meaning  of  the  whole 
paragraph  or  chapter  in  which  they  occur,  or  to  gain  no 
definite  idea  from  it  whatever.  This  may  be  partly  the  fault 
of  the  author,  for  if  a  book  is  intended  as  an  elementary 
text-book,  it  is  his  business  not  to  use  words  in  these  new 
senses  without  saying  something  about  it.  But  it  is  also 
largely  the  fault  of  the  student  himself.  He  knows  that  the 
author  is  trying  to  convey  some  definite  meaning;  and  if  he 
took  the  trouble  to  inquire  what  that  meaning  really  is, 
instead  of  being  satisfied  with  his  work  when  he  has  read  the 
words  or  learned  to  jumble  some  of  them  together,  he  would 
see  very  easily  that  some  of  these  words  must  be  used  in  a 
strange  sense. ' 

The  same  trouble  occurs  also  very  frequently  in  history 
and  literature.  If  a  book  was  written  more  than  a  century 
ago,  many  of  its  words  will  have  been  used  in  a  sense  with 
which  we  are  no  longer  familiar;  and  here  again  unless  we 
are  very  careful  we  are  likely  to  misunderstand  the  author's 
meaning  completely.  What,  for  example,  is  the  meaning 
of  the  italicised  words  in  the  following  passages  from  the 
Bible  ?  "I  may  tell  all  my  bones:  they  look  and  stare  upon 
me  "  (Ps.  22:17).  "I  prevented 'the  dawning  of  the  morning, 
and  cried:  I  hoped  in  thy  word  "  (Ps.  119:147).  "But 
unto  thee  have  I  cried,  O  Lord;  and  in  the  morning  shall 
my  prayer  prevent  thee  "  (Ps.  88:  13).  '  That  I  may  show 
all  thy  praises  within  the  ports  of  the  daughter  of  Sion  " 
(Ps.  9:  14,  Prayer-book  version).  "  My  daughter  is  grievously 
vexed  with  a  devil  "  (Matt.  15:  22).  What  also  is  meant  by 
the  word  '  let ',  by  the  word  '  meat  '  in  the  phrase  '  meat 
and  drink  ',  by  '  rod  '  and  '  staff '  in  Ps.  23,  and  by  the 
phrase  '  What  have  I  to  do  with  thee  ?  '  What  did  the 


BLUNDERS   OF   INTERPRETATION.  15 

Biblical  writers  mean  by  a  '  prophet ',  by  '  cherubim  ',  and 
by  a  'penny'  as  the  word  is  used  in  the  story  of  the  Good 
Samaritan?  What  is  meant  in  Magna  Charta  when  it  says, 
"  No  free  man  shall  be  taken  or  imprisoned  .  .  .  but  by  lawful 
judgment  of  his  peers  "  ?  * 

If  words  do  not  mean  anything  when  they  are  taken  in  a 
sense  with  which  we  are  familiar,  we  can  be  sure  that  the 
author  was  either  writing  nonsense  or  using  them  in  some 
sense  with  which  we  are  not  familiar.  But  even  when  they 
do  mean  something  when  taken  in  our  ordinary  sense,  that 
may  not  be  what  the  author  meant  them  to  mean.  Hence 
students  of  historical  methods  say  that  we  must  not  read 
some  old  writings  for  the  purpose  "  of  extracting  information 
from  it  without  any  thought  of  first  ascertaining  exactly  what 
was  in  the  author's  mind  ".  If  we  do,  we  are  sure  to  give 
the  author's  words  our  meaning  instead  of  his.  Therefore 
we  must  make  it  a  rule  to  understand  the  exact  meaning  of 
what  is  said  "  before  asking  what  can  be  extracted  from  it 
for  the  purpose  of  history  ",f  or  for  any  other  purpose. 
The  Bible,  for  example,  is  full  of  the  deepest  truths;  but 
most  of  us  read  it  without  finding  them  simply  because  the 
rhythm  is  pleasant  and  the  words  are  familiar  and  it  never 
occurs  to  us  to  inquire  whether  or  not  the  men  who  wrote 
them  meant  to  say  anything  that  we  have  not  thought  already, 
and  if  they  did,  what  it  is. 

This  finding  of  the  meaning,  even  where  it  seems  plain 
enough  already,  is  no  mere  perfunctory  matter.  To  be  sure 


*  A  student  of  philosophy  should  pay  particular  attention  to  the  mean- 
ing of  such  words  as  '  Idea  ',  '  Perception  ',  '  Impression  ',  '  Reflection  ', 
as  used  by  Locke,  by  Berkeley,  and  by  Hume;  the  phrase  '  Moral  Philos- 
ophy '  as  used  by  Hume  and  his  contemporaries  ;  '  Conceive  '  as  used  in 
different  contexts  by  Herbert  Spencer  ;  '  Substanz  ',  '  Wirklichkeit ', 
'  Realitat ',  '  Noumenon  ',  and  '  Ding  an  sich  '  as  used  by  Kant,  and  the 
like. 

fLanglois-Seignobos,  "Introduction  to  the  Study  of  History",  pp. 
143-146  (Henry  Holt  &  Co.,  1898). 


1 6  THE  MEANINGS   OF  WORDS. 

that  we  have  done  it  aright  we  should  have  studied  the 
language  of  the  time  and  country  as  well  as  of  the  author 
himself.  But  the  essence  of  the  method  is  always  the  same 
— to  find  a  meaning  or  a  set  of  meanings  for  a  Avord  which 
will  enable  us  to  give  a  reasonable  interpretation  to  every 
passage  in  which  it  occurs.* 

But  we  need  not  go  to  science  and  literature  to  find  words 
misunderstood.  Such  misunderstandings  occur  continually 
in  every-day  life,  and  often  do  great  mischief. 

There   are    various    ways    in   which   words    may  become 

ambiguous,  or  get  several  meanings  that  are  liable 
How  words  '         °         T  ,     . 

become  am-  to  be  confused.      Jevons  gives  three  of  them  as 
bifuous.         ,     . 

follows: 

1.  From  the  accidental  confusion  of  different  words;  e.g. , 
the  adjective  mean  may  signify  medium  or  average  (from  the 
French  moyen),  or  despicable  (from  the  Anglo-Saxon  gemoene) ; 
light  may  signify  the  opposite  of  heaiy  (from  the   same  root 
as  levis)  or  the  opposite  of  dark  (from  the  same  root  as  lux). 

2.  From  the  transfer  of  meaning  from  the  original  objects 
to  others  associated  with  them;  e.g. ,  the  words  house,  court, 
church,  all  mean  either  a  place  or  those  that  meet  there. 

3.  From  the  transfer  of  meaning  to  analogous    objects. 
The  word  sweet  is  applied  to  sounds  and  innumerable  other 
things  that  give  pleasant  feelings,  though  none  of  these  feel- 
ings is  similar  in  any  other  respect  to  sweet  tastes.    Similarly 
the/00/  of  a  mountain,  the  hand  of  a  clock  and  the  leg  of  a 
table  do  not  bear  any  close  resemblance  to  human  limbs, 
but  in  certain  respects  they  answer  the  same  purpose.      As 
Whately  puts  it,  "  leg  :  animal  ::  supporting  stick  :  table  ". 
It  is  by  the  same  kind  of  analogy  that  recent  writers  speak 
of  society  as  an  organism. 

*  "  'These  studies  of  words ',  said  Fustel  de  Coulanges,  'have  a  great 
importance  in  historical  science.  A  badly  interpreted  term  may  be  a 
source  of  serious  error.'  And,  in  fact,  simply  by  a  methodical  applica- 
tion of  interpretative  criticism  to  a  hundred  words  or  so,  he  succeeded  in 
revolutionizing  the  study  of  the  Merovingian  epoch."  (Op.  cit.,  p.  150.) 


BLUNDERS   OF  INTERPRETATION.  17 

The  more  difference  there  is  between  a  word's  different 
meanings  the  more  likely  we  are  to  discover  the  ambiguity 
before  it  has  done  much  harm.  When  any  one  what  am- 
speaks  of  '  the  church  '  we  are  not  likely  to  con-  are'most 
fuse  a  building  with  the  group  of  people  that  danfi:er( 
worships  in  it.  The  context  soon  shows  which  he  means. 
But  we  very  well  might  confuse  different  larger  and  smaller 
groups  of  worshippers.  When  we  are  told  that  such  and 
such  is  the  custom  or  practice  of  '  the  Church  '  it  might  be 
hard  to  tell  whether  the  speaker  was  referring  to  the  com- 
municants or  voting  members  of  a  certain  particular  congre- 
gation, to  the  congregation  as  a  whole,  to  the  denomination, 
to  a  particular  group  of  denominations,  excluding  Roman 
Catholics,  Unitarians,  or  others  that  the  speaker  regarded  as 
heretical,  to  the  Western  Church  in  all  its  branches,  or  to 
the  whole  body  of  those  who  call  themselves  Christians. 
Even  when  we  are  sure  which  of  these  bodies  he  means  we 
may  still  be  unable  to  say  what  proportion  of  the  individuals 
in  the  body  he  intends  to  include  when  he  says  that  such  is 
the  practice  of  '  the  Church  '.  One  person  might  say  that 
something  was  the  practice  of  '  the  Church  '  if  it  were  done 
habitually  by  a  third  of  the  individual  members;  another 
might  not  say  so  unless  it  were  done  by  two-thirds  or  three- 
quarters  ;  and  still  a  third  might  deny  that  anything  was  the 
practice  of  '  the  Church  '  even  if  it  were  done  habitually  by 
all  the  members  so  long  as  it  was  not  done  officially  by  the 
body  as  an  organized  whole  under  the  direction  of  the  proper 
officers. 

Words  which  are  ambiguous  because  we  cannot  tell  how 
much  or  how  little  they  are  intended  to  include  are  called 
Vague.  The  word  Church  in  the  last  example  was  vague 
because  it  did  not  show  precisely  what  individuals  the  speaker 
intended  to  include  in  the  group  that  he  used  it  to  indicate. 
In  other  cases  the  ambiguity  is  about  relations:  a  word  is 
used  to  indicate  a  group  of  them,  but  we  cannot  tell  precisely 
what  they  are.  This  vagueness  is  characteristic  of  many  of 


1 8  THE  MEANINGS   OF  WORDS. 

our  commonest  words,  and  is  explained  by  the  way  in  which 
we  begin  to  use  them. 

"  In  Geometry  .  .  .  we  learn  the  definitions  of  the  words 
used,  point,  line,  parallel,  etc.,  before  we  proceed  to  use 
them.  But  in  common  speech,  we  learn  words  first  in  their 
application  to  individual  cases.  Nobody  ever  defined  good 
to  us,  or  fair,  or  kind,  or  highly  educated.  We  hear  the 
:  words  applied  to  individual  objects;  we  utter  them  in  the 
same  connection;  we  extend  them  to  other  objects  that  strike 
us  as  like  without  knowing  the  precise  points  of  likeness  that 
the  convention  of  common  speech  includes.  The  more 
I  exact  meaning  we  learn  by  induction  from  individual  cases. 
Ugly,  beautiful,  good,  bad — we  learn  the  words  first  as  appli- 
cable to  things  and  persons:  gradually  there  arises  a  more  or 
less  definite  sense  of  what  the  objects  so  designated  have 
in  common.  The  individual's  extension  of  the  name 
proceeds  upon  what  in  the  object  has  most  impressed  him 
when  he  caught  the  word ;  this  may  differ  in  different  in- 
dividuals; the  usage  of  neighbors  corrects  individual  eccen- 
tricities. " 

The  more  complex  and  intangible  the  object  or  relation 
which  a  word  is  used  to  indicate  the  greater  is  the  danger  of 
misunderstanding  from  its  ambiguities.  '  Take  such  words 
as  monarchy,  tyranny,  civil  freedom,  freedom  of  contract, 
landlord,  gentleman,  prig,  culture,  education,  temperance,  gen- 
erosity. .  .  .  Let  two  men  begin  to  discuss  any  proposition 
in  which  any  such  word  is  involved,  and  it  will  often  be 
found  that  they  take  the  word  in  different  senses.  If  the 
relation  expressed  is  complex,  they  have  different  sides  or 
lines  of  it  in  their  minds;  if  the  meaning  is  an  obscure 
quality,  they  are  guided  in  their  application  of  it  by  different 
outward  signs. 

"  Monarchy,  in  its  original  meaning,  is  applied  to  a  form 
of  government  in  which  the  will  of  one  man  is  supreme,  to 
make  laws  or  break  them,  to  appoint  or  dismiss  officers  of 
state  and  justice,  to  determine  peace  or  war,  without  control 


BLUNDERS   OF   INTERPRETATION.  19 

of  statute  or  custom.  But  supreme  power  is  never  thus 
uncontrolled  in  reality;  and  the  word  has  been  extended  to 
cover  governments  in  which  the  power  of  the  titular  head  is 
controlled  in  many  different  modes  and  degrees.  The  exist- 
ence of  a  head,  with  the  title  of  King  or  Emperor,  is  the 
simplest  and  most  salient  fact;  and  wherever  this  exists  the 
popular  concept  of  a  monarchy  is  realized.  The  President 
of  the  United  States  has  more  real  power  than  the  Sovereign 
of  Great  Britain;  but  the  one  government  is  called  a 
Republic  and  the  other  is  called  a  Monarchy.  People  dis- 
cuss the  advantages  and  disadvantages  of  monarchy  with- 
out first  deciding  whether  they  take  the  word  in  its  etymo- 
logical sen-se  of  unlimited  power,  or  its  popular  sense 
of  titular  kingship,  or  its  logical  sense  of  power  definitely 
limited  in  certain  ways.  And  often,  in  debate,  monarchy 
is  really  a  singular  term  for  the  government  of  Great 
Britain. 

"Culture,  religious,  generous,  are  names  for  inward  states 
or  qualities:  with  most  individuals  some  simple  outward  sign 
directs  the  application  of  the  word — it  may  be  manner,  or 
bearing,  or  routine  observances,  or  even  nothing  more  sig- 
nificant than  the  cut  of  the  clothes  or  of  the  hair.  Small 
things  undoubtedly  are  significant,  and  we  must  judge  by 
small  things  when  we  have  nothing  else  to  go  by;  but  instead 
of  trying  to  get  definite  conceptions  for  our  moral  epithets, 
and  suspending  judgment  till  we  know  that  the  use  of  the 
epithet  is  justified,  the  trifling  superficial  sign  becomes  for 
us  practically  the  whole  meaning  of  the  word.  We  feel  that 
we  must  have  a  judgment  of  some  sort  at  once  :  only  simple 
signs  are  suited  to  our  impatience. 

"  It  was  with  reference  to  this  state  of  things  that  Hegel 
formulated  his  paradox  that  the  true  abstract  thinker  is  the 
plain  man  who  laughs  at  philosophy  as  what  he  calls  abstract 
and  unpractical.  He  holds  decided  opinions  for  or  against 
this  or  the  other  abstraction,  freedom,  tyranny,  revolution, 
reform,  socialism,  but  what  these  words  mean  and  within 


20  THE   MEANINGS   OF  WORDS. 

\     what  limits  the  things  signified  are  desirable  or  undesirable 
he  is  in  too  great  a  hurry  to  pause  and  consider."  * 

Here  is  an  example  of  some  of  the  mischief  done  by 
ambiguous  words  in  economics:  "The  discussion  of  'the 
relations  of  labor  and  <oapital  '  has  not  hitherto  been  very 
fruitful.  It  has  been  confused  by  ambiguous  definitions, 
and  it  has  been  based  upon  assumptions.  .  .  . 

"  Let  us  first  examine  the  terms. 

"  (i)  Labor  means  properly  toil,  irksome  exertion,  expen- 
diture of  productive  energy. 

"  (2)  The  term  is  used,  secondly,  by  a  figure  of  speech, 
and  in  a  collective  sense,  to  designate  the  body  of  persons 
who,  having  neither  capital  nor  land,  come  into  the  produc- 
tive organization  offering  productive  services  in  exchange 
for  means  of  subsistence.  These  persons  are  united  by 
community  of  interest  into  a  group,  or  class,  or  interest, 
and  when  interests  come  to  be  adjusted,  the  interests  of 
this  group  will  undoubtedly  be  limited  by  those  of  other 
groups. 

"  (3)  The  term  labor  is  used,  thirdly,  in  a  more  restricted, 
very  popular  and  current,  but  very  ill-defined  way,  to  desig- 
nate a  limited  sub-group  among  those  who  live  by  contribut- 
ing productive  efforts  to  the  work  of  society.  Every  one  is 
a  laborer  who  is  not  a  person  of  leisure.  Public  men,  or 
other  workers,  if  any,  who  labor  but  receive  no  pay,  might 
be  excluded  from  the  category,  and  we  should  immediately 
pass,  by  such  a  restriction,  from  a  broad  and  philosophical 
to  a  technical  definition  of  the  labor  class.  Ikit  merchants, 
bankers,  professional  men,  and  all  whose  labor  is,  to  an 
important  degree,  mental  as  well  as  manual,  are  excluded 
from  this  third  use  of  the  term  labor.  The  result  is,  that 
the  word  is  used,  in  a  sense  at  once  loosely  popular  and 
strictly  technical,  to  designate  a  group  of  laborers  who 
separate  their  interests  from  those  of  other  laborers.  Whether 
farmers  are  included  under  '  labor  '  in  this  sense  or  not  I 

*  Minto's  Logic,  pp.  83-87  (Scribners,  1893). 


BLUNDERS   OF   INTERPRETATION.  21 

have  not  been  able  to  determine.  It  seems  that  they  are  or 
are  not,  as  the  interests  of  the  disputants  may  require.  .  .  . 

"  (i)  Capital  is  any  product  of  labor  which  is  used  to 
assist  production. 

"  (2)  This  term  also  is  used,  by  a  figure  of  speech,  and  in 
a  collective  sense,  for  the  persons  who  possess  capital,  and 
who  come  into  the  industrial  organization  to  get  their  living 
by  using  capital  for  profit.  To  do  this  they  need  to 
exchange  capital  for  productive  services.  These  persons  con- 
stitute an  interest,  group,  or  class,  although  they  are  not 
united  by  any  such  community  of  interest  as  laborers,  and, 
in  the  adjustment  of  interests,  the  interest  of  the  owners  of 
capital  must  be  limited  by  the  interests  of  other  groups. 

"  (3)  Capital,  however,  is  also  used  in  a  vague  and  pop- 
ular sense  which  it  is  hard  to  define.  In  general  it  is  used, 
in  this  sense,  to  mean  employers  of  laborers,  but  it  seems  to 
be  restricted  to  those  who  are  employers  on  a  large  scale. 
It  does  not  seem  to  include  those  who  employ  only  domestic 
servants.  Those  also  are  excluded  who  own  capital  and 
lend  it,  but  do  not  directly  employ  people  to  use  it. 

"  It  is  evident  that  if  we  take  for  discussion  '  capital  and 
labor',  if  each  of  the  terms  has  three  definitions,  and  if  one 
definition  of  each  is  loose  and  doubtful,  we  have  everything 
prepared  for  a  discussion  which  shall  be  interminable  and 
fruitless,  which  shall  offer  every  attraction  to  undisciplined 
thinkers,  and  repel  everybody  else."  * 

Here  is  another  example  from  the  same  source:  "  There 
is  no  possible  definition  of  '  a  poor  man  '.  A  pauper  is  a 
person  who  cannot  earn  his  living;  whose  productive  powers 
have  fallen  positively  below  his  consumption:  who  cannot, 
therefore,  pay  his  way.  .  .  .  But  he  is  not  the  '  poor  man  '. 
The  '  poor  man  '  is  an  elastic  term,  under  which  any  number 
of  social  fallacies  may  be  hidden.  Neither  is  there  any 
possible  definition  of  '  the  weak  '.  Some  are  weak  in  one 

*  Sumner,  "What  Social  Classes  Owe  to  Each  Other,"  pp.  81-84. 
(New  York :  Harper  &  Bros. ) 


22  THE   MEANINGS   OF   WORDS. 

way,  and  some  in  another;  and  those  who  are  weak  in  one 
sense  are  strong  in  another.    .   .    . 

"  Under  the  names  of  the  poor  and  the  weak,  the  negli- 
gent, shiftless,  inefficient,  silly,  and  imprudent  are  fastened 
upon  the  industrious  and  prudent  as  a  responsibility  and  a 
duty.  On  the  one  side,  the  terms  are  extended  to  cover  the 
idle,  intemperate,  and  vicious,  who,  by  the  combination, 
gain  credit  which  they  do  not  deserve,  and  which  they  could 
not  get  if  they  stood  alone.  On  the  other  hand,  the  terms 
are  extended  to  include  wage-receivers  of  the  humblest  rank, 
who  are  degraded  by  the  combination.  The  reader  who 
desires  to  guard  himself  against  fallacies  should  always 
scrutinize  the  terms  '  poor  '  and  '  weak  '  as  used,  so  as  to 
see  which  or  how  many  of  these  classes  they  are  made  to 


cover. 


* 


When  two  persons  use  words  in  different  senses  it  is  not 
surprising  that  one  should  reject  a  statement  which  the  other 
accepts.  What  is  surprising  is  that  we  fail  so  often  to 
discover  that  our  difference  is  not  about  the  external  facts 
at  all,  but  only  about  the  meaning  of  the  words.  Often  a 
discussion  does  end  in  our  looking  up  words  in  a  dictionary. 
But  it  ought  not  to  end  there;  for  if  we  fully  realized  the 
difference  between  the  words  that  we  happened  to  use  and 
the  things  and  relations  that  we  used  them  to  indicate,  we 
should  come  back  from  the  dictionary  and  ask  what  was  the 
real  point  of  difference  between  us  with  reference  to  these 
things  and  relations.  For  surely  it  was  these  and  not  the 
meaning  of  words  that  we  meant  to  discuss. 

Vague  and  ambiguous  words  not  only  make  us  misunder- 
stand others.  They  do  worse,  and  make  us  misunderstand 
Blunders  of  ourselves  and  commit  bad  blunders  in  conse- 
n  erence.  quence.  Since  a  word  is  a  mark  intended  "  to 
raise  in  our  mind  a  thought  like  to  some  thought  which 
we  had  before",  we  naturally  take  it  for  granted  that  any 
thought  which  the  word  does  raise  in  our  mind  is  the  one 
*  Sumner,  1.  c.,  pp.  20,  21. 


BLUNDERS   OF   INFERENCE.  23 

which  we  had  before  when  we  used  it ;  and  if  we  have  con- 
cluded that  a  statement  is  true  we  suppose  it  to  be  true  abso- 
lutely, without  its  ever  occurring  to  us  that  it  might  be  per- 
fectly true  when  the  words  are  taken  in  one  sense  and 
utterly  false  when  they  are  taken  in  another.  But  if  words 
are  ambiguous  and  we  take  them  in  one  sense  when  we  are 
inquiring  into  their  truth  and  then  take  them  in  a  different 
sense  when  we  are  asking  what  can  be  inferred  from  their 
truth,  it  is  evident  that  we  may  easily  reach  some  conclusion 
which  we  never  would  have  reached  if  the  two  different 
thoughts  had  not  happened  to  be  expressed  or  suggested 
by  the  same  word.  Sometimes  these  plays  on  words  are  so 
obvious  that  they  are  only  intended  to  amuse  a  hearer. 
Sometimes  they  are  intended  to  puzzle  him;  it  is  perfectly 
evident  that  the  conclusion  does  not  follow;  but  the  words 
make  it  seem  as  though  it  should;  and  the  puzzle  is  to 
explain  why.  Often,  however,  the  words  really  do  deceive 
both  speaker  and  hearer.  As  Bacon  says:  "  Men  imagine 
that  their  minds  have  the  command  of  language;  but  it  often 
happens  that  language  bears  rule  over  their  minds."  Here 
are  some  examples  of  various  kinds. 

We  know  that  we  ought  to  control  our  tempers,  and  we 
happen  to  have  expressed  this  by  the  statement  that  it  '  is 
wrong  to  be  irritated  ',  and  to  remember  the  words.  A  phy- 
sician finds  that  a  patient  who  needs  absolute  quiet  is  being 
constantly  disturbed  by  various  noises,  and  in  stating  the 
fact  he  happens  to  say  in  his  technical  language  that  the 
patient  is  constantly  '  irritated '.  This  is  the  word  used  in 
the  formula  that  we  happen  to  remember:  it  is  wrong  to  be 
irritated  ;  and  so,  without  stopping  to  ask  what  the  physician 
means  by  it,  we  jump  to  the  conclusion  that  the  patient  is 
constantly  doing  something  wrong. 

'  Lincoln  says  you  cannot  fool  all  the  people  all  the  time ; 
but  Mr.  G.  at  his  bargain-sales  fools  all  the  people  and  he 
fools  them  every  time;  therefore  Lincoln  was  wrong.' 
Here  the  trouble  lies  in  the  ambiguity  of  the  phrase  '  all  the 


24  THE   MEANINGS   OF  WORDS. 

people  '  and  in  the  assumption  that  '  all  the  time '  means  the 
same  as  '  every  time  ' .  '  All  the  people  '  in  the  second  sentence 
means  all  the  people  at  the  bargain-sale  ;  but  Lincoln  meant 
by  it  all  the  people  in  the  country.  '  Every  time  '  as  it  is  used 
here  means  every  time  Mr.  G.  has  a  bargain-sale;  but  'all 
the  time'  as  Lincoln  used  the  phrase  means  for  a  long  con- 
tinuous period  in  the  life  of  a  nation. 

'  A  saving  man  is  a  blessing  to  the  community  ;  a  miser  is 
a  saving  man ;  therefore  a  miser  is  a  blessing  to  the  com- 
munity.' Here  the  word  '  saving '  may  be  ambiguous  or  it 
may  not.  If  we  understand  by  '  a  saving  man  '  in  the  first 
sentence  any  one  whatever  who  saves  his  money  instead  of 
spending  it,  then  the  conclusion  follows  from  the  facts 
assumed.  But  it  is  more  likely  that  any  one  who  grants  the 
truth  of  the  first  statement  is  thinking  of  '  a  saving  man  '  as 
one  who  exercises  reasonable  economy  in  contrast  to  a  spend- 
thrift. If  this  is  so,  we  make  him  say  more  than  he  intended 
if  we  extend  the  meaning  of  the  word  '  saving  '  so  as  to  include 
those  who  exercise  unreasonable  economy ;  and  thus  the 
argument  is  unfair. 

'  A  teacher  must  know  how  to  teach  ;  Mr.  R. ,  who  has 
just  taken  up  the  work,  does  not  know  how  to  teach  ;  there- 
fore Mr.  R.  cannot  be  a  teacher.'  Here  there  are  several 
ambiguities.  '  A  teacher  '  may  mean  any  one  who  earns  his 
living  in  a  schoolroom,  or  it  may  mean  a  '  true  '  or  ideal 
teacher,  When  we  say  he  must  know  how  to  teach  we  may 
mean  that  if  he  does  not  he  is  not  a  teacher  (as  when  we  say 
a  square  must  have  four  sides);  we  may  mean  that  he  ought 
to  know  ;  or  we  may  mean  that  if  any  one  does  not  know  he 
will  not  be  allowed  to  attempt  the  work.  '  Know  how  to 
teach  '  is  ambiguous  in  two  respects.  In  the  first  place,  to 
'  know  how  '  may  mean  to  understand  the  principles  involved, 
it  may  mean  to  have  a  certain  amount  of  practical  skill 
whether  one  understands  the  principles  or  not,  and  it  may 
mean  to  have  both  principles  and  skill.  In  the  second  place 
the  phrase  '  know  how '  is  vague  because  it  does  not  tell  us 


BLUNDERS   OF   INFERENCE.  25 

how  much  knowledge  the  speaker  has  in  mind.  When  he 
says  that  a  teacher  must  '  know  how  '  to  teach,  does  he  mean 
that  he  must  be  able  to  do_it  according  to  the  latest  approved 
principle,  or  does  he  merely  mean  that  he  must  be  able  to  do 
it  as  well  as  any  intelligent  person  could?  Even  'teach' 
is  ambiguous.  Does  it  mean  merely  to  give  instruction  in 
certain  subjects,  or  does  it  mean  .also  to  keep  order  in  the 
schoolroom  and  instil  good  morals  and  manners  ?  The  phrase 
'  cannot  be  '  in  the  conclusion  of  the  argument  has  much  the 
same  ambiguities  as  '  must '  in  the  first  part  of  it.  Does  it 
mean  '  certainly  is  not ',  'will  not  be  permitted  to  be',  or 
'  cannot  become '  ?  If  the  premises  mean  that  an  ideal 
teacher  has  a  certain  amount  of  knowledge  or  skill  and  that 
Mr.  R.  has  not,  the  conclusion  follows  that  Mr.  R.  is  not  an 
ideal  teacher  ;  but  it  does  not  follow  that  Mr.  R.  is  not 
earning  his  living  in  a  schoolroom,  that  he  is  excluded  from 
the  teaching  profession,  or  that  he  cannot  become  an  ideal 
teacher ;  and  so  with  the  other  meanings  of  the  various 
sentences. 

The  following  curious  arguments  are  taken  from  a  book 
written  to  prove  that*  a  lie  is  never  justifiable,  and  have 
doubtless  imposed  upon  a  large  number  of  readers  as  well  as 
the  author  himself.* 

A)  "  Truth  is,  so  to  speak,  the  very  substratum  of  Deity.  .  .  . 
As  there  is  no  God  but  the  true  God,  so  without  truth  there 
is  and  can  be  no  God." 

B)  "As  Christ  is  Truth,  those  who  are  in  Christ  must  never 
violate  the  truth.  .  .  .  This  would  seem  to  be  explicit  enough 
to  shut  out  the  possibility  of  a  justifiable  lie." 

C)  "We  cannot  conceive  of  God  as  God,  unless  we  con- 
ceive of  him  as  the  true  God,  and  the  God  of  truth.    If  there 
is  any  falsity  in  him,  he  is  not  the  true  God.    Truth  is  of  God's 
very  nature.    To  admit  in  our  thought  that  a  lie  is  of  God,  is 

*Trumbull,  "A  Lie  Never  Justifiable",  pp.  135,  145-6,  223.  224. 
The  first  extract  is  given  as  a  quotation  from  Hodge's  "Systematic  The- 
ology ",  and  the  second  as  a  summary  of  Martensen. 


26  THE  MEANINGS   OF   WORDS. 

to  admit  that  falsity  is  in  him,  or,  in  other  words,  that  he  is 
a  false  God." 

D)  "  A  lie  is  the  opposite  of  truth,  and  a  being  who  will 
lie  stands  opposed  to  God,  who  by  his  very  nature  cannot  lie. 
Hence  he  who  lies  takes  a  stand,  by  that  very  act,  in  opposition 
to  God.  Therefore  if  it  be  necessary  at  any  time  to  lie,  it  is 
necessary  to  desert  God  and  be  in  hostility  to  him  so  long 
as  the  necessity  for  lying  continues." 

Let  us  examine  these  arguments.  In  A  the  author  sup- 
poses his  reader  to  take  for  granted  that  'There  is  no  God 
but  the  true  God  '.  From  this  it  is  supposed  to  follow  that 
'  Without  truth  there  is  and  can  be  no  God  '  ;  from  this  that 
'Truth  is,  so  to  speak,  the  very  substratum  of  Deity';  and 
from  this  that  a  lie  is  never  justifiable  under  any  circum- 
stances. But  what  do  these  words  all  mean  ?  When  he 
expects  every  one  to  admit  that  '  there  is  no  God  but  the  true 
God  ',  he  must  mean  by  it  that  there  is  no  God  but  the  god 
that  really  exists,  whatever  we  may  call  him,  and  whatever 
his  nature  may  be.  If  the  next  step  follows  from  this,  '  With- 
out truth  there  is  and  can  be  no  God  ',  these  words  must  be 
taken  to  mean  that  if  there  is  no  reality — if  there  is  nothing 
real — there  is  and  can  be  no  real  God.  This  same  thought 
is  expressed  in  the  next  set  of  words  :  'Truth' — that  is  to 
say,  reality — '  is  the  very  substratum  of  Deity  '.  But  from 
this  fact  that  God  would  not  exist  if  nothing  real  existed  it 
surely  does  not  follow  that  a  lie  is  never  justifiable.  The 
only  reason  that  it  seems  to  follow  is  that  the  word  '  truth  ' 
is  ambiguous,  and  when  the  author  says  that  '  truth  '  is 
the  very  substratum  of  Deity  he  forgets  that  when  this  was 
proved  it  meant  that  reality  was  the  substratum  of  Deity,  and 
now  he  takes  it  to  mean  that  always  making  true  statements 
and  disapproving  of  every  false  statement  is  '  the  very  sub- 
stratum of  Deity';  and  from  this  it  follows  that  a  lie  is  never 
justifiable.  Hence  we  have  to  take  the  words  in  one  sense 
in  order  that  they  should  follow  from  what  every  one  is  sup- 
posed to  admit,  and  take  them  in  quite  another  sense  in  order 


BLUNDERS   OF   INFERENCE.  27 

that  the  conclusion  should  follow  from  them.  So  long  as  we 
think  only  of  the  words  it  is  possible  to  be  deceived  by  the 
argument.  When  we  ask  their  precise  meaning  and  look 
carefully  at  the  things  about  which  they  are  supposed  to  tell  it 
is  not. 

In  B  what  is  meant  by  the  statement  that  Christ  is  '  Truth  '  ? 
It  certainly  does  not  mean  that  he  is  an  accurate  statement. 
Hence  this  must  be  taken  more  or  less  metaphorically  to 
mean  that  in  his  life  there  is  to  be  found  a  revelation  of  the 
deepest  spiritual  truths,  that  he  is  a  true  or  genuine  mani- 
festation of  God,  or  something  of  that  sort.  Christ  then 
revealing  the  true  spiritual  life,  it  follows  that  '  those  who  are 
in  Christ  must  never  violate  the  truth',  that  is,  it  follows 
that  those  who  are  in  communion  with  him  should  not  do 
anything  inconsistent  with  that  highest  spiritual  life.  But 
why  does  this  'shut  out  the  possibility  of  a  justifiable  lie' 
unless  we  assume  what  was  to  be  proved,  that  a  lie  never  is 
justifiable,  or  in  accordance  with  the  highest  spiritual  life? 
Here  again  it  is  only  the  ambiguity  of  the  word  '  truth  '  that 
makes  the  conclusion  seem  to  follow.  Unless  the  statement 
that  those  who  are  in  Christ  must  never  violate  the  truth 
means  what  I  have  said,  it  does  not  follow  from  what  was 
said  about  Christ ;  and  unless  the  sense  is  then  twisted  and 
the  statement  is  taken  to  mean  that  they  must  never  tell  a  lie 
under  any  circumstances  whatever,  the  conclusion  does  not 
follow  from  it. 

In  C  there  is  the  same  play  on  the  words  '  true  '  and 
'  truth  '  as  in  A,  and  a  similar  play  on  the  words  '  false'  and 
'falsity'.  This  becomes  very  apparent  if  we  omit  these 
ambiguous  words  altogether  and  substitute  for  them  the 
synonyms  that  seem  to  express  the  meaning  most  accurately 
in  each  individual  case.  The  passage  will  then  read  some- 
thing like  this  :  '  We  cannot  conceive  of  God  as  God  unless 
we  conceive  of  him  as  the  real  God,  and  the  God  of  reality 
(or  who  is  trustworthy,  or  who  never  approves  of  a  lie).  If 
there  is  any  unreality  (or  untrustworthiness}  in  him,  he  is  not 


28  THE   MEANINGS   OF   WORDS. 

the  real  (or  trustworthy}  God.  Reality  (or  trustworthiness) 
is  of  God's  very  nature.  To  admit  in  our  thought  that  a  lie 
is  of  (i.e.,  approved  under  any  circumstances  by)  God,  is  to 
admit  that  unreality  is  in  him,  or,  in  other  words,  that  he  is 
a  fictitious  God.'  So  long  as  we  do  not  make  any  attempt  to 
interpret  the  words  the  conclusion  may  seem  to  be  proved  ; 
but  when  we  drop  the  words  and  consider  only  the  relations 
that  they  ought  to  be  used  to  point  out  it  is  perfectly  evident 
that  it  is  not. 

In  D  the  ambiguity  lies  in  the  word  '  opposed  '  and  its 
derivatives.  When  we  say  that  '  a  lie  is  the  opposite  of 
truth '  we  mean  that  a  false  statement  is  unlike  a  true  one 
and  can  be  contrasted  with  it  just  as  large  can  be  contrasted 
with  small ;  and  if  God  '  by  his  very  nature  cannot  lie  ',  then 
a  being  who  can  and  will  lie  '  stands  opposed  to  God '  in  the 
sense  that  the  two  can  be  contrasted,  just  as  a  large  man  can 
be  contrasted  with  a  small  One.  It  does  not  follow  in  the 
slightest  that  there  is  any  'hostility'  between  them.  The 
only  reason  that  the  conclusion  appears  to  follow  is  that  the 
words  'opposite',  'opposed'  and  'opposition'  are  all  de- 
rived from  the  same  root,  and  \ve  therefore  assume  when  they 
are  being  used  that  they  all  have  essentially  the  same  mean- 
ing without  stopping  to  ask  what  that  meaning  is  until  the 
verbal  manipulation  is  over.  Then  we  are  told  that  '  in  op- 
position '  means  'in  hostility',  and  we  cannot  deny  it.  As 
a  piece  of  reasoning  this  sort  of  verbal  jugglery  is  almost  on 
a  plane  with  that  which  proves  something,  I  have  forgotten 
what,  by  saying  that  a  beehive  is  a  bee-holder,  a  beholder  a 
spectator,  and  a  specked  'tater  a  bad  vegetable. 

This  last  example  shows  the  danger  of  so-called  Parony- 
mous  terms.  When  a  word  is  not  ambiguous  in  itself  we  may 
introduce  an  ambiguity  by  substituting  for  it  some  other  word 

derived  from  the  same  root  and  so  constructed  that 
Paronymous 

terms.  it  seems  to   point   to  exactly  the  same   relations, 

when  it  does  not.  We  have  a  perfect  right  to  say,  '  Romeo  is 
in  love;  lovers  are  impetuous;  therefore  Romeo  is  im- 


HOW  TO   DEAL  WITH   AMBIGUITIES.  29 

pettious';  because  the  words  'in  love'  and  'lover'  point  to 
precisely  the  same  state  of  mind.  But  we  have  no  right  to 
say,  '  Schemers  are  not  to  be  trusted  ;  this  man  has  a  scheme  ; 
therefore  he  is  not  to  be  trusted  ' ;  for  one  is  not  a  '  schemer  ' 
unless  his  '  schemes '  are  rather  dishonest,  and  are  so  habit- 
ually. So  likewise  a  man  who  is  once  drunken  or  who  once 
lies  is  not  necessarily  a  drunkard  or  a  liar.  Words  like  these, 
which  appear  to  correspond  in  meaning  but  really  do  not, 
are  quite  common,  e.g. :  art,  artful;  design,  designing, 
faith,  faithful ;  presume,  presumption  ;  king,  kingly  ;  probable, 
probability ;  child,  childish. 

When  \ve  are  confronted  with  arguments  which  turn  upon 
some  ambiguous  word  we  do  not  usually  see  what  the  trouble 

is  all   at  once  :    but  we  often  do   have  a  vague 

.      How  to 

feeling  that  there  is  something  wrong;  and  this  deal  with 

,    ambiguities. 

ought  to  be  sufficient  to  make  us  go  back  and 

examine  all  the  words  on  which  the  argument  seems  to 
turn.  The  surest  way  to  test  the  argument  is  to  put  it  into 
new  words  altogether,  taking  care  that  each  one  of  them 
shall  indicate  something  perfectly  definite.  Since  all  correct 
inference  is  based  upon  the  nature  and  relations  of  the 
things  in  question,  and  not  upon  the  relations  of  the 
words  in  which  we  happen  to  speak  of  them,  this  method 
of  getting  rid  of  the  questionable  words  is  perfectly  legiti- 
mate and  reasonable.  When  this  has  been  done  and  we 
realize  exactly  what  the  relations  in  question  are,  we  may 
then  go  back  to  the  old  words  and  show  how  they  seemed  to 
indicate  first  one  and  then  another.  If  we  wish  to  avoid 
making  such  blunders  ourselves,  we  should  pursue  much  the 
same  method,  and  make  sure  that  our  argument  depends 
upon  the  relations  of  things  themselves  and  not  upon  the 
accidents  of  language  by  seeing  whether  it  will  seem  to  hold 
no  matter  what  language  we  use  to  denote  these  relations. 

When  words  are  vague  or  otherwise  ambiguous,  it  is  usu- 
ally wise  for  the  person  who  uses  them  in  a  given  connection 
to  announce  the  exact  meaning  which  he  intends  them  to 


30  THE   MEANINGS   OF   WORDS. 

express.  When  he  does  this  he  is  said  to  define  them.  A 
Definition,  therefore,  is  a  statement  of  the  meaning  of  a  word 

as  used   in  a  given  connection,   or  a  statement 
Definition.        ,  ... 

that    tells   what    qualities    or   other  relations  an 

object  must  have  in  order  that  the  word  defined  should  be 
properly  applied  to  it.  By  the  aid  of  definitions  the  same 
word  can  be  used  in  different  senses  in  different  connections 
without  confusion. 

When  a  word  of  doubtful  meaning  has  not  been  defined  by 
the  user  the  only  course  for  the  hearer  or  reader  is  to  define 
it  for  himself  by  comparing  the  various  passages  in  which  it 
occurs.  He  must  try  to  find  some  definite  meaning  which 
will  fit  them  all.  This  is  what  the  makers  of  every  dictionary 
have  to  do.  By  a  definite  meaning  I  mean  of  course  a 
definite  relation  that  the  word  is  used  to  denote,  not  merely 
a  definite  set  of  phrases  to  put  after  it  in  a  definition  whether 
they  mean  anything  or  not.  We  have  not  found  the  meaning 
for  the  word  '  toves  '  merely  because  we  have  learned  to  say, 
"  They  are  something  like  badgers — they  are  something  like 
lizards — and  they  are  something  like  corkscrews".  If  a 
word  has  several  distinct  meanings,  or  if  the  meaning  is  vague, 
the  effort  to  find  one  definite  meaning  which  will  fit  the  con- 
text in  every  case  will  soon  make  this  plain. 

To  find  a  definite  meaning  for  every  word  and  every  state- 
ment in  the  books  that  one  studies  is  no  easy  task,  and  when 
any  one  first  undertakes  to  do  it  he  will  probably  be  disap- 
pointed to  find  how  little  ground  he  can  cover.  But  unless  a 
person  seeks  one  he  cannot  understand  the  book  thoroughly, 
and  unless  he  does  it  often  enough  to  feel  confidence  in  his  own 
work  he  cannot  tell  the  difference  between  a  book  that  means 
something  and  one  that  does  not.  He  will  not  be  able  to 
'understand'  the  latter,  or  get  definite  thoughts  out  of  it, 
but  he  will  not  be  able  to  tell  whether  it  is  because  of  his  own 
stupidity  or  because  there  are  no  definite  thoughts  there  to 
get;  and  if  he  has  not  this  ability  to  discriminate,  he  is  likely 
to  be  the  victim  of  any  incoherent  writer  whose  words  are 


HOW   TO   FRAME   DEFINITIONS.  31 

sufficiently  high-sounding. J  This  ability  to  interpret  what 
one  reads  or  hears  and  discriminate  between  sense  and  non- 
sense is  one  of  the  most  essential  aims  of  all  education,  and 
a  person  who  has  not  taken  the  trouble  to  acquire  it  ought 
not  to  call  himself  educated. 

When  we  have  found  the  meaning  of  a  word  and  come  to- 
state  it  two  things  are  essential:  to  hpj>rf  rise  and  to  be_simi)le. 

To  be  precise  is  to  tell  exactly  what  the  word  means 

— - —  — . — —-  How  to 

— no  more  and  no  less;  to  state  the  characteristics   frame 

r  ..          .        .  ri-ii  •  i-      definitions, 

of  an  object;  in  virtue  of  which  the  name  is  appli- 
cable, with  perfect  definiteness.  We  must  not  define  a  net 
as  something  made  out  of  string  with  holes  in  it,  or  as  some- 
thing to  catch  fish  with.  For  a  net  is  not  necessarily  made 
out  of  string  or  used  to  catch  fish,  and  things  might  be  made 
of  string  and  have  holes  in  them,  or  be  used  to  catch  fish, 
without  being  nets.  In  the  same  way  we  should  not  define 
man  as  the  animal  that  laughs,  for  though  man  may  be  the 
only  animal  that  laughs,  it  is  not  laughter  that  makes  him  man 
and  entitles  him  to  the  name.  He  would  remain  man  if  he 
never  laughed  again.  So,  we  should  not  define  virtue  as  the 
only  thing  which  makes  one  truly  and  permanently  happy, 
or  acid  as  that  which  turns  blue  litmus  paper  red  ;  for  virtue 
might  still  be  virtue  if  it  ceased  to  make  us  happy,  and  the 
word  acid  would  be  quite  as  applicable  to  various  substances 
if  litmus  paper  had  never  existed. 

To  be  simple  in  a  definition  is  to  frame  it  in  such  a  way 
that  it  will  immediately  mean  something  to  the  people  for 
whom  it  is  intended.  Dr.  Johnson  defines  a  net  as  something 
reticulated  and  decussated,  with  interstices  between  the  inter- 
sections ;  and  Herb"ert~Spencer  defines  evolution  as  "an  inte- 
gration of  matter  and  concomitant  dissipation  of  motion, 
during  which  the  matter  passes  from  an  indefinite,  inco- 
herent homogeneity  to  a  definite,  coherent  heterogeneity,  and 
during  which  the  retained  motion  undergoes  a  parallel  trans- 
formation." These  definitions  are  precise  and  to  the  expert 
they  may  be  simple,  but  to  ordinary  people  they  are  not. 


32  THE   MEANINGS   OF   WORDS. 

Simplicity   and    precision    are    difficult    to    unite,  but   with 
patience  the  union  cau..nearly  always  be  made. 

There  is  an  old  rule  that  definitions  should  be  by  genus 
and  differeniice.  This  means  that  it  is  not  necessary  or  desir- 
able to  enumerate  every  single  attribute  of  the  things  denoted 
by  the  name  defined.  It  is  sufficient  to  tell  what  class  they 
belong  to  and  how  they  differ  from  other  members  of  that 
class.  If  we  are  defining  the  word  '  bloodhound  '  we  should 
say  that  blpo_clhounds  are  a  certain  specified  kind  of  dog.  It 
is  not  necessary  to  say  that  they  are  living  things,  belonging 
to  the  animal  kingdom,  and  possessed  of  a  backbone,  mouth, 
eyes,  ears,  teeth,  and  paws.  These  attributes  and  a  hundred, 
others  are  all  implied  by  the  generic  term  '  dog '. 

To  define  a  term  by  itself  or  by  some  other  equally  obscure 
word  from  the  same  root,  e.g.,  'a  preacher  is  one  who 
preaches',  is  practically  the  same  as  not  to  define  it  at  all.  It 
adds  neither  precision  nor  simplicity.  But  if  two  words 
from  the  same  root  do  not  indicate  precisely  the  same  rela- 
tions it  may  be  proper  to  define  one  by  means  of  the  other 
and  some  modifying  phrase,  e.g.,  'a.  preacher  is  one  who 
preaches  by  profession ',  '  a  liar  is  one  who  tells  lies  habit- 
ually'. Again,  we  are  likely  to  lose  rather  than  gain  in  both 
precision  and  simplicity  when  we  define  in  metaphorical 
language,  as  when  we  say  that  words  are  barbed  arrows,  the 
soul  is  life's  star,  truth  is  the  food  of  the  soul,  or  the  camel  is 
the  ship  of  the  desert.  The  metaphors  may  be  useful,  but 
not  as  definitions. 

Definitions  are  usually  supplemented  by  examples,  diagrams, 
or  other  illustrations.  These  do  not  make  the  definition  any 

more  accurate,  for  they  give  only  one  case  out  of 
Illustrations.  r  ..... 

many  that  fall  within  it,  and  unless  .some  explana- 
tion is  added,  they  do  not  show  exactly  where  the  dividing 
line  is.  But  they  do  make  the  definition  easier  to  understand, 
because  they  turn  one's  attention  in  the  right  direction. 
When  we  know  some  of  the  things  which  a  boundary  is 
intended  to  include  we  are  better  prepared  to  learn  precisely 


ILLUSTRATIONS.  33 

where  jtbat  boundary  is.  Because  examples  give  this  kind  of 
preparation  it  is  often  wise  to  put  some  of  them  before  the 
formal  definition. 

The  illustration  chosen  should  be  typical.  If  we  try  to 
prepare  for  the  definition  of  vjrtue  by  an  example,  we  should 
choose  some  act  or  character  that  is  recognized  as  virtuous  by 
everybody  ;  somethingjyell  within  the  class,  and,  if  possible, 
something  of  which  virtue  is  the  most  striking  feature.  To 
prepare  for  the  definition  of  a  fish  we  should  not  draw  an  eel. 
It  looks  too  much  like  a  snake.  After  the  definition  is  given, 
however,  and  its  general  purport  is  understood  it  is  often  wise 
to  give  an  example  of  something  that  falls  within  it  and  of 
something  else  quite  like  it  that  falls  without,  and  then  explain 
why  it  is  that  the  one  is  included  and  the  other  not.  When 
one  is  making  a  contrast  of  this  sort  one  might  well  use  an 
eel  to  illustrate  the  difference  between  a  fish  and  a  snake,  or 
a  whale  to  illustrate  the  difference  between  a  fish  and  a 
mammal.  The  nearer  we  get  to  the  boundary  on  any  side 
the  easier  it  is  to  understand  a  description  of  that  particular 
part  of  it. 

When  an  example  is  not  so  striking  as  to  be  unmistakable 
we  should  take  pains  to  make  clear  in  precisely  what  respect 
it  illustrates.  It  will  not  do  to  say,  '  The  subject  of  a 
sentence  is  the  name  of  the  thing  spoken  about,  e.g. ,  John 
struck  James  '.  We  should  underline  the  word  '  John  ',  put 
it  in  quotation-marks,  or  indicate  in  some  other  way  that  it  is 
that  word  that  is  the  subject,  and  not  the  real  John  or  the 
word  'James'.  Similarly  we  cannot  explain  what  a  house 
is  by  merely  handing  some  one  a  picture  and  leaving  him  to 
wonder  whether  the  house  is  the  thing  in  the  background 
with  windows  or  the  thing  in  the  foreground  with  ears. 

The  reason  why  the  common  uneducated  person  does  not 
recognize  the  importance  of  understanding  the  meaning  of 
words  precisely  is  that  it  is  really  not  very  important  for  his 
purposes.  To  play  out  of  doors,  to  find  one's  way  along  the 
street  and  notice  what  people  are  doing  there,  to  buy  clothes 


34  THE   MEANINGS   OF   WORDS. 

or  groceries  :    all  these  are  very  concrete  performances,  and 

any  one  can  carry  them  on  or  tell  about  them 
Where  /  . 

precision  is  afterwards  fairly  well  without  a  painstaking  choice 
-needed  most.  c  ,  ,,,..  ,  ,  .  .  .  ' 

of  words.      With  the  work    of  school    and    the 

first  year  or  two  of  college  the  need  for  a  careful  examination 
and  selection  of  words  becomes  more  apparent  ;  and  yet 
only  a  fair  amount  of  care  and  skill  in  the  use  of  words  is 
required  to  tell  about  the  concrete  facts  of  history  and 
geography,  describe  the  processes  involved  in  a  chemical 
experiment,  and  even  translate  concrete  statements  from  a 
foreign  language,  without  confusion.  But  when  we  come 
to  the  abstract  sciences,  and  have  to  deal,  not  with  the 
surface  of  things,  but  with  their  deeper  relations,  the  case 
is  very  different.  The  political  economist  must  make 
sharp  distinctions  between  wealth,  capital,  and  money  ;  the 
psychologist,  between  sensation  ana  perception,  concep- 
tion and  imagination,  illusion,  delusion,  and  hallucination  ; 
the  student  of  ethics,  between  intention  and  motive,  pleasure 
and  satisfaction ;  the  theologian,  between  wrong  and  sin, 
providence  and  predestination,  substance  and  personality ; 
the  lawyer,  between  torts  and  crimes,  corporations  and  part- 
nerships, and  so  on.  Here  the  things  under  discussion  are 
not  visible  and  tangible,  and  we  cannot  explain  what  we  are 
talking  about  by  merely  pointing  the  finger.  It  takes  much 
skill  to  talk  or  think  about  them  without  confusion,  and  the 
only  way  to  be  sure  of  doing  so  is  to  make  absolutely  clear- 
cut,  precise,  and  rigid  definitions,  and  keep  them  in  mind 
throughout  the  whole  discussion.  Such  definitions  are  not 
conventional  ornaments  at  the  head  of  a  page,  they  are 
necessities. 

Although  the   meaning    of  every   word,  and  therefore    all 
definition,  has   reference   to  things,  we  do  not  define  things. 

Names  are  defined  when  we  tell  what  they  mean  ; 

classes  may  be  said  to  be  '  defined  '  when  we  point 
out  their  boundaries  ;  things  may  be  described  in  sentences  but 
never  defined,  for  no  words  can  make  them  any  more  definite 


CAUTION.  35 

than  they  are.  The  question  sometimes  raised  whether  we 
define  names  or  things  depends,  as  Mill  has  shown,  upon  the 
fact  that  some  definitions  carry  with  them  the  assumption  of 
the  thing's  existence  in  the  real  word  (e-g.,  any  definition 
of  cow  or  horse),  while  others  do  not  (e.g.,  a.  definition  of 
a  dragon  or  of  a  perfect  man).  But  in  ench  case  it  is  the 
meaning  of  the  word,  not  the  thing,  with  which  thejJefmitjon 
is  primarily  concerned.  To  be  sure  in  the  former  case  we 
can  prove  a  definition  to  be  wrong  by  showing  that  it  does 
not  agree  with  the  thing ;  but  that  is  because  the  name  stands 
for  the  thing,  and  if  the  definition  does  not  agree  with  the 
thing  it  cannot  correctly  explain  the  name. 

In  the  following  chapters  it  will  be  necessary  to  define  a 
considerable  number  of  logical  terms.  The  definitions  given 
were  made  with  care,  but  doubtless  some  of  them  are  incor- 
rect. Every  reader  is  urged  to  make  out  as  well  as  he  can 
from  the  explanations,  the  illustrations,  and  the  definitions 
themselves  exactly  what  each  one  of  them  was  intended  to 
express,  and  then  go  back  and  see  whether  it  really  did  ex- 
press it  or  not,  and  if  not  why  not.  This  will  help  him  to 
understand  the  book  and — what  is  far  more  important — it 
will  give  him  good  general  practice  in  the  accurate  interpre- 
tation and  use  of  words.  To  increase  the  opportunities  for 
this  practice  there  are  among  the  exercises  at  the  back  of  the 
book  a  large  number  of  definitions  of  these  same  logical 
terms  which  are  incorrect,  and  the  reader  is  advised  to  go 
over  as  many  of  them  as  possible  and  state  clearly  and  ex- 
actly what  is  wrong  with  each.  This  he  will  find  much 
harder  than  to  merely  score  them  out  and  put  correct  ones  in 
their  places ;  but  the  practice  is  correspondingly  better. 


CHAPTER   III. 
THE  MEANING   OF   STATEMENTS   AS   A   WHOLE. 

WHEN  we  know  the  literal  meaning  of  every  individual 
word  and  phrase  used  by  a  speaker  or  writer  there  is  still 
danger  of  misinterpreting  him  ;  for  often  people  do  not  in- 
tend what  they  say  to  be  taken  seriously  and  literally. 

Not  seriously,  for  he  may  be  using  some  customary  phrase 
which  is  hardly  intended  to  mean  anything  at  all.  If  a 
letter  begins  with  the  phrase  '  Dear  Sir '  and  ends  with 
Conventional  ' Yours  faithfully '  or  '  Your  obedient,  humble 
phrases.  servant',  or  even  if  the  words  are  somewhat 
more  effusive,  we  must  not  conclude  that  the  writer  neces- 
sarily meant  any  more  than  to  be  polite.  He  may  be  writing 
to  his  worst  enemy.  And  of  course  there  are  corresponding 
forms  and  phrases  in  every  age  and  country.  When  a 
Spaniard  tells  you  that  his  house  is  yours  he  does  not 
expect  you  to  ask  for  the  title-deeds.  Even  official  documents 
are  not  free  from  such  polite  phrases.  The  Grand  Remon- 
strance was  really  an  indictment  containing  over  two  hundred 
counts  against  the  King  himself,  drawn  up  in  1641  when 
the  Parliament  and  King  were  on  the  verge  of  civil  war, 
and  yet  the  petition  with  which  it  was  presented  begins  as 
follows:  "  J\Tost  Gracious  Sovereign,  Your  Majesty's  most 
humlk  and  faithful  subjects  the  Commons  in  this  present 
Parliament  assembled,  do  with  much  thankfulness  and  joy 
acknowledge  the  great  mercy  and  favor  of  Cod  in  giving 
your  majesty  a  safe  and  peaceable  return  out  of  Scotland  into 

36 


OBLIQUE   SENSES.  37 

the  Kingdom  of  England,  where  the  pressing  dangers  and 
distempers  of  the  State  have  caused  us  with  much  earnestness 
to  desire  the  comfort  of  your  royal  presence,  and  likewise  the 
unity  and  justice  of  your  royal  authority  ' ' ,  etc. 

In  the  United  States  such  terms  as  '  liberty'  and  'home' 
have  been  used  so  much  for  all  sorts  of  political  purposes  that 
they  have  ceased  to  have  any  very  definite  meaning  when 
they  are  used  in  political  and  social  controversies.  The  other 
day,  for  example,  I  read  in  a  newspaper  editorial  that  the 
Boers  in  the  present  war  (1900)  were  fighting  for  '  their 
liberty  and  their  homes  '.  Of  course  this  is  only  a  rhetorical 
way  of  saying  that  they  are  fighting  for  a  certain  form  of 
political  independence,  but  a  reader  who  had  no  other  sources 
of  information  might  very  well  conclude  from  it  that  the 
British  government  really  wanted  to  take  forcible  possession 
of  private  property  and  drag  the  owners  off  into  slavery. 

When  a  person  expects  something  that  he  says  to  be 
taken  seriously,  he  may  still  not  expect  to  have  it  taken  lit- 
erally. "It  is  possible  that  he  may  have  used  Obliaue 
some  expressions  in  an  oblique  sense  ;  there  are  senses- 
several  kinds  of  cases  where  this  occurs  :  allegory  and  sym- 
bolism, jests  and  hoaxes,  allusion  and  implication,  even  the 
ordinary  figures  of  speech,  metaphor,  hyperbole,  litotes.  In 
all  these  cases  it  is  necessary  to  pierce  through  the  literal 
meaning  to  the  real  meaning,  which  the  author  has  purposely 
disguised  under  an  inexact  form."  *  The  devil  quoted  scrip- 
ture accurately  enough,  but  took  it  altogether  too  literally 
when  he  set  Jesus  on  the  pinnacle  of  the  temple  and  said  to 
him,  "  If  thou  art  the  Son  of  God  cast  thyself  down  :  for  it 
is  written,  He  shall  give  his  angels  charge  concerning  thee : 
and  on  their  hands  they  shall  bear  thee  up,  lest  haply  thou 
dash  thy  foot  against  a  stone  ". 

Many  other  examples  of  these  oblique   senses  are  to  be 

*  Langlois-Seignobos,  p.  151.  Hoaxes  might  have  been  omitted. 
They  can  hardly  be  said  to  contain  a  '  real  meaning  disguised  under  an 
inexact  form '. 

4  a  i   j'^y.-i  V*  ~1<*  > 

•  it  t  *  t jk;<o 


38       THE   MEANING   OF   STATEMENTS   AS   A   WHOLE. 

found  in  the  Bible.  The  Beast  and  the  Scarlet  Woman  in 
the  Apocalypse  and  the  visions  in  the  second  part  of  Daniel 
are  certainly  not  intended  to  be  taken  literally.  And  the 
books  of  Job  and  Jonah  ?  Shall  they  be  taken  in  the  direct 
sense  as  history  or  in  the  oblique  sense  as  allegory?  Surely 
we  must  ask  what  a  document  really  means  before  we  can  ask 
whether  it  is  true  or  demand  that  any  one  accept  the  truth 
which  it  contains. 

"  A  parallel  difficulty  occurs  in  the  interpretation  of  illus- 
trative monuments;  the  representations  are  not  always  to  be 
taken  literally.  In  the  Behistun  monument  Darius  tramples 
the  vanquished  chiefs  under  foot  :  this  is  a  metaphor.  Me- 
diaeval miniatures  show  us  persons  lying  in  bed  with  crowns 
on  their  heads  :  this  is  to  symbolize  their  royal  rank  ;  the 
painter  did  not  mean  that  they  wore  their  crowns  to  sleep 
in."* 

Exaggeration  as  a  form  of  oblique  speech  demands  special 
consideration.  It  is  so  common  with  some  people  that  they 
constantly  assume  that  what  they  say  will  be  discounted,  and 
Ex  _  do  not  realize  all  that  is  meant  by  the  statements 
ation.  of  others  unless  they  are  likewise  exaggerated.  A 

picture  that  pleases  them  is  the  most  beautiful  they  ever  saw, 
a  pleasant  evening  is  the  best  time  they  ever  had  in  their 
lives,  and  so  on.  A  person  who  says  what  he  means,  no 
more  and  no  less,  may  very  well  be  deceived  into  attaching 
altogether  too  much  importance  to  the  statements  of  such 
people  ;  and  they,  on  the  contrary,  are  likely  to  attach  alto- 
gether too  little  to  his.  If  he  says  that  some  men  are  honest, 
they  assume  that  he  means  to  say  that  most  are  not ;  if  he 
gives  qualified  praise  they  assume  that  he  does  not  mean 
to  praise  at  all  or  that  he  means  to  damn  with  faint  praise. 

*  Langlois-Seignobos.— "  Only  one  general  principle  [for  detection 
of  oblique  meanings]  can  be  laid  down,  and  that  is,  that  when  the 
iit'-ral  sense  is  absurd,  incoherent,  or  obscure,  or  in  contradiction  with 
the  ideas  of  the  author  or  the  facts  known  to  him,  then  we  ought  to 
presume  an  oblique  sense."  (Op.  cit.,  p.  152.) 


AMPHIBOLOGY.  39 

Hence  there  is  always  danger  of  misunderstandings  when 
persons  accustomed  to  accurate  statements  are  interpreting 
those  who  are  not,  and  vice  versa. 

Exaggeration,  however,  is  not  only  a  matter  of  personal 
habit.  Under  the  name  hyperbole  it  is  recognized  as  a  cor- 
rect form  of  literary  expression;  and  not  to  make  allowance 
for  it  is  to  misinterpret  the  passage  in  which  it  occurs,  e.g.  : 
"  If  a  man  can  number  the  dust  of  the  earth,  then  shall  thy 
seed  also  be  numbered  " ;  "  He  was  owner  of  a  piece  of  ground 
not  larger  than  a  Lacedemonian  letter";  "  He  was  so  gaunt, 
the  case  of  a  flageolet  was  a  mansion  for  him  ". 

In  connection  with  this  interpretation  of  statements  as  a 
whole,  it  is  customary  for  writers  on  logic  to  point  out  several 
kinds  of  blunders,  to  which  they  have  given  characteristic 
names,  as  follows. 

To  commit  the  '  Fallacy  of  Amphibology  '  is  to  misinterpret 
a  sentence  because  its  construction  is  ambiguous.  The  tradi- 
tional examples  are  from  ambiguous  oracular  deliv- 

.  Amphibology. 

erances,  e.g.,  '  Aio  te  /bacida  Romanes  vmccre 

posse  '  (I  say  that  you  Avicus  the  Romans  are  able  to  con- 
quer); 'The  D;ike  yet  lives  that  Henry  shall  depose'.  Ex- 
quisite care  w  is  needed  to  make  such  ambiguous  construc- 
tions as  these,  but  most  of  those  we  meet  are  the  result  of  gross 
carelessness  e.g.:  '  Wanted — a  piano,  by  a  young  lady  made 
of  mahogany  ';  '  lie  finished  his  business  and  returned  on 
Wednesday  ';  '  Twice  two  and  three  ':  '  He  who  necessarily 
goes  or  stays  (i.e.,  who  necessarily  goes  or  who  necessarily 
stays)  is  not  a  free  agent,  you  must  necessarily  go  or  stay 
(i.e.,  take  the  alternative),  therefore  you  are  not  a  free 
agent  '.*  The  confusion  can  always  be  remedied  by  a  recon- 
struction of  the  sentence  ;  often  by  a  mere  change  in  punc- 
tuation or  in  the  position  of  a  word. 

The  name  '  Fallacy  of  Accident '  is  applied  to  three  differ- 
ent kinds  of  blunders : 

i)  When  a  statement  about  the  mere  substance  of  some 
*  Whately  gives  this  last  as  a  fallacy  of  composition. 


40      THE   MEANING    OF   STATEMENTS   AS   A  WHOLE. 

individual  thing  is  interpreted  as  referring  to  its  condition 
(accident)  as  well,  e.g.,  '  What  you  bought  yester- 
day you  eat  to-day;  raw  meat  is  what  you  bought 

yesterday;  therefore  you  eat  raw  meat  to-day'. 

2)  When  an  abstract  statement  about  some  of  the  relations 
or  essential  characteristics  of  a  certain  kind  of  thing  is  in- 
terpreted as  a  concrete  statement  about  every  thing  of  the 
kind  in  all  its  relations  (accidents),  *  e.g. ,  '  Meat  is  good  for 
food,  this  spoiled  horse-flesh  is  meat,  therefore  this  spoiled 
horse-flesh  is  good  for  food  ';    '  I  do  not  admire  tall  women, 
A.  B.  is  a  tall  woman,  therefore  I  do  not  admire  A.  B.'.      In 
these  examples  the  major  premises  really  refer  to  '  Meat  as 
such  '  or  '  the  essential  characteristics  of  meat  ',  '  tall  women 
as  such  '  or  '  tallness  in  women  '.  * 

3)  When  any  loose  statement  really  intended  to  tell  only 
what   is  true  '  under  ordinary  conditions  '   or   '  other    things 
being  equal  '  or  '  usually  '  (though  such  phrases  are  omitted) 
is  interpreted  as  though  it  meant  to  tell  what  is  true  always, 
no  matter  how  unusual  the  conditions,  e.g.,  '  Strychnine  is  a 
deadly  poison,  therefore  this  minute  dose  is  Mire  to  poison  me  '; 
'  The  use  of  medicine  is  to  be  avoided  (when  possible),  there- 
fore this  sick  man  must  not  touch  it';  'Corporal  punishment 
is  debasing    (as  a   rule),  therefore   this  bully   should  not  be 
thrashed  '. 

In  all  of  these  examples  the  Fallacy  of  Accident  has  been 
Direct  ;  the  reasoning  has  been  from  a  statement  concerning 
the  substance,  essence  or  rule,  without  reference  to  any  acci- 
dent or  special  condition,  to  a  case  in  which  such  accident  is 
present  (a  dido  sirnplicilcr  ad  dictum  sccundiim  quid].  But 
corresponding  to  each  of  the  three  kinds  of  direct  fallacy 
there  is  also  the  Converse  Fallacy  of  Accident  (a  dicto  sccun- 
dum  quid  ad  dictum  sim/sliciler)  where  the  accident  or  special 
condition  is  implied  in  the  major  premise  anil  omitted  in  the 

*  In  the  first  ca<e  the  accident  is  contrasted  with  Aristotle's  'mate- 
rial '  or  I^ickc's  '  real  '  essence  ;  in  the  latter  with  Aristotle's  •  formal  ' 
or  Locke's  •  nominal '  essence. 


ACCIDENT.  41 

minor  and  conclusion,  e.g. :  (i)  'What  you  liked  yesterday 
you  like  to-day,  you  liked  this  (fresh)  bread  yesterday,  there- 
fore you  like  this  same  (stale)  bread  to-day';  (2)  '  I  admire 
A.B.  and  C.D.;  A.B.  and  C.D.  are  tall  women  ;  therefore  I 
admire  tall  women'  (as  such);  (3)  '  Strychnine  is  a  magnificent 
remedy  (for  certain  diseases  and  in  certain  doses),  A.B.  needs 
a  remedy,  therefore  he  should  take  strychnine'.* 

Direct  or  converse  fallacies  of  accident  of  the  first  class  are 
comparatively  rare  and  trivial.  Those  in  the  two  other 
classes  (which  are  not  always  easily  distinguished  from  each- 
other)  can  be  avoided  by  insisting  upon  accurate  statements  or 
explanations  if  the  speaker  is  present  and  willing  to  make  them; 
but  when  authoritative  interpreters  are  not  at  hand  they  may 
cause  interminable  discussions  and  disputes.  Everybody 
admits,  for  example,  that  lying  is  wrong  ;  but  does  that  mean 
that  every  act  that  involves  a  lie  is  wrong,  or  only  that  lies 
as  such  are  wrong,  and  acts  that  involve  a  lie  are  wrong  pro- 
vided that  there  is  no  other  and  more  important  moral  considera- 
tion involved?  If  we  interpret  the  law  in  the  first  sense  it  is 
wrong  to  lie  to  a  madman  or  a  murderer  to  save  the  life  of  a 
child  ;  if  in  the  second  it  is  right,  provided  that  the  obliga- 
tion to  save  an  innocent  life  is  greater  than  the  obligation  to 
always  refrain  from  lying,  and  that  to  tell  a  lie  is  the  only 
available  way  of  saving  it.  Human  relations  are  so  complex 
that  we  can  only  discuss  one  aspect  of  them  at  a  time  ;  and 
it  may  very  well  be  that  some  moral  laws  nt  least  have  reference 
not  to  acts  as  a  whole  but  to  aspects  of  them,  and  that  in  in- 
terpreting such  laws  one  aspect  must  be  balanced  against 
another  and  the  one  indissoluble  concrete  act  judged  by  the 
most  important  moral  consideration  involved. 

The  interpretation  of  moral  laws  is  a  question  of  ethics,  but 

*  The  article  '  a '  lends  itself  easily  to  this  kind  of  confusion.  '  I  ad- 
mire a  tall  woman  '  may  mean  that  I  admire  some  individual  woman 
who  happens  to  be  tall  or  that  I  admire  tallness  in  women.  It  is  this 
confusion  that  gives  point  to  the  time-honored  conundrum,  '  What 
makes  more  noise  than  a  pig  under  a  gate  ?  '  '  Two  pigs.' 


42       THE   MEANING   OF   STATEMENTS   AS   A  WHOLE. 

if  we  accept  a  law  in  one  sense  and  then  apply  it  in  the  other 
we  commit  the  logical  fallacy  of  accident. 

The  fallacy  of  '  Accent '  is  essentially  a  fallacy  of  interpre- 
tation. It  consists  in  misinterpreting  an  author  (i)  by  un- 
duly accenting  some  particular  word  in  a  sentence, 
e.g. ,  '  Thou  shalt  not  bear  false  witness  against  thy 
neighbor',  or  '  Thou  shalt  riot  bear  false  witness  against  thy 
neighbor'  ;  *  or  (2)  by  taking  passages  out  of  their  immediate 
context,  e.g. ,  proving  that  Dr.  Watts  believed  in  dog-fights  be- 
cause he  said  "  Let  dogs  delight  to  bark  and  bite  ",  or  proving 
future  punishment  by  John  xv.  6  :  "  And  men  gather  them 
and  cast  them  into  the  fire  rind  they  are  burned",  or  by 
Matt.  xxii.  13  :  "  Ca^t  him  into  outer  darkness  ;  there  shall  be 
weeping  and  gnashing  of  teeth"  ;  or  (5)  by  appealing  to 
some  particular  passage,  even  a  long  one,  though  it  may  be 
contrary  to  the  whole  spirit  of  the  author  quoted.  This  is  a 
form  of  the  fallacy  of  which  the  members  of  any  Christian 
sect  might  very  well  accuse  the  members  of  all  the  others. 
The  controversy  as  to  the  whole  spirit  of  the  gospels  which 
such  an  accusation  would  raise  would  be  much  more  profit- 
able than  any  amount  of  quibbling  over  a  few  proof  texts. 

A  remarkably  clear  exposition  cf  tins  fallacy  is  given  in 
the  preface  to  Matthew  Arnold's  "  Literature  and  Dogma", 
from  which  I  quote  a  few  sentences.  It  is  of  course  his 
account  of  the  fallacy  in  which  we  are  interested,  not  his 
views  on  the  Bible. 

"  The  homo  nnius  lilri,  the  man  of  no  range  in  his  reading, 
must  almost  inevitably  misunderstand  the  Bible,  cannot  treat 
it  largely  enough,  must  be  inclined  to  treat  it  all  alike,  and 
to  press  every  word.  ...  lie  has  not  enough  experience  of 
the  way  in  which  men  have  thought  and  spoken,  to  feel  what 

*  Jevons  quotes  the  passage  from  the  Hook  of  Kin^s.  '  And  he  spake 
to  his  sons,  saying.  Saddle  me  the  ass.  And  they  saddled  him'.  But 
tli ih  is  surely  a  case  of  amphibology.  The  acvent  on  the  word  'him' 
changes  the  meaning  of  the  passage  only  because  it  changes  the  ante- 
cedent to  which  the  pronoun  refers. 


ACCENT.  43 

the  Bible-writers  are  about ;  to  read  between  the  lines,  to 
discern  where  he  ought  to  rest  with  his  whole  weight,  and 
where  he  ought  to  pass  lightly.  .  .  .  And  thus  we  come  back 
to  our  old  remedy  of  cijllut'e, — knowing  the  best  that  has  been 
thought  and  known  in  the  world  ;  which  turns  out  to  be  in 
another  shape,  and  in  particular  relation  to  the  Bible  :  getting 
the  power,  through  reading,  to  estimate  the  proportion  and  rela- 
tion in  what  we  read.  If  we  read  but  a  very  little,  we  nat- 
urally want  to  press  it  all;  if  we  read  a  great  deal,  we  are 
willing  not  to  press  the  whole  of  what  we  read,  and  we  learn 
what  ought  to  be  pressed  and  what  not.  Now  this  is  really 
the  very  foundation  of  any  sane  criticism.  .  .  .  Things  are  on 
such  a  scale,  and  progress  is  so  gradual,  and  what  one  man 
can  do  is  so  bounded,  that  the  moment  we  press  the  whole  of 
what  any  writer  says,  we  fall  into  error.  He  touches  a  great 
deal  :  the  thing  to  know  is  where  he  is  all  himself  and  his 
best  self,  where  he  sho\vs  his  power,  where  he  goes  to  the 
heart  of  the  matter,  where  he  gives  us  what  no  other  man 
gives  us  or  gives  us  so  well." 

The  danger  of  this  fallacy  of  accent  is  well  recognized  by 
jurists,  and  by  their  rules  of  evidence  they  try  to  guard 
against  it.  "  '  I  have  always ',  said  Lord  Tenterden,  '  acted 
most  strictly  on  the  rule,  that  what  is  in  writing  shall  only 
be  proved  by  the  writing  itself.  My  experience  has  taught 
me  the  extreme  danger  of  relying  on  the  recollection  of 
witnesses,  however  honest,  as  to  the  contents  of  written  in- 
struments ;  they  may  be  so  easily  mistaken  that  I  think  the 
purposes  of  justice  require  the  strict  enforcement  of  the 
rule'  ".  This  is  one  reason.  But  then  Tenterden  goes  on 
to  say:  "  'By  applying  the  rule  to  such  cases  the  Court  ac- 
quires a  knowledge  of  the  whole  contents  of  the  instrument, 
which  may  have  a  different  effect  from  the  statement  of  a 
part.'  "  * 

So  with  confessions  and  other  statements  against  the  inter- 
est of  the  person  who  makes  them.  The  law  gives  them 
*  Greenleaf,  "Law  of  Evidence",  Vol.  I,  Sec.  88. 


44      THE   MEANING   OF   STATEMENTS   AS   A  WHOLE. 

great  weight,  but  it  also  insists  that  they  shall  not  be  garbled. 
"  In  the  proof  of  confessions,  as  in  the  case  of  admissions  in 
civil  cases,  the  whole  of  what  the  person  said  on  the  subject 
at  the  time  of  making  the  confession  should  be  taken  to- 
gether. ...  It  is  not  reasonable  to  assume  that  the  entire 
proposition,  with  all  its  limitations,  was  contained  in  one 
sentence.  .  .  .  Unless  the  whole  is  received  and  considered, 
the  true  meaning  and  import  of  the  part  which  is  good  evi- 
dence against  him  cannot  be  ascertained."  * 

On  the  same  principle  it  is  a  rule  of  evidence  that  if  a 
witness  tells  about  a  part  of  any  conversation  the  lawyer  who 
cross-examines  him  has  a  right  to  ask  about  any  other  part  of 
the  same  conversation. 

The  difference  between  the  fallacy  of  Accent  and  the  fal- 
lacy of  Accident  in  the  broader  sense  of  each  is  this  :  the 
former  misinterprets  a  writer  by  confusing  incidental  state- 
ments with  essential ;  the  latter  confuses  aspects  of  things  or 
situations  (or  statements  about  such  aspects)  with  the  things 
or  situations  (or  statements  about  them)  as  a  whole,  f 

*  Greenleaf,  op.  cit,  Sec.  218. 

•f  Whether  we  should  call  the  over-emphanzing  of  some  one  aspect  of 
the  moral  code  accent  or  accident  would  thus  depend  upon  whether 
we  regarded  the  law  as  a  revelation  each  part  of  which  should  be  inter- 
preted with  reference  to  the  whole,  or  as  an  analysis  of  conduct  into 
various  good  and  bad  aspects,  several  of  which  may  be  combined  in  the 
complex  whole.  An  aspect  of  a  law  taken  for  the  whole  law  is  ac- 
cent ;  an  aspect  of  an  act  taken  for  the  whole  act  is  accident. 


CHAPTER   IV. 
DIVISION  AND   CLASSIFICATION. 

To  avoid  confusion  in  the  use  of  names  we  must  define 
them;  but  all  definition  of  names  involves  a  classification  of 
objects.  If  the  words  '  animal ',  '  red  ',  '  verte-  Relatlon  to 
brate '  have  any  definite  meaning  at  all  there  definition, 
must  be  some  things  to  which  they  can  be  properly  applied 
and  some  things  to  which  they  cannot,  and  the  things  to 
which  any  one  of  them  can  be  applied  must  all  have  the 
qualities  or  relations  which  the  name  implies,  and  therefore 
resemble  each  other  in  this  respect,  while  the  things  to 
which  it  cannot  be  properly  applied  must  all  resemble  each 
other  in  not  having  these  qualities  or  relations.  Hence  every 
time  we  use  a  name  we  imply  the  existence  of  two  classes  of 
things :  those  that  have  the  quality  or  relation  which  the 
name  implies  and  those  that  have  not.  To  define  a  name 
is  to  distinguish  between  these  two  classes,  and  the  more 
clearly  \ve  understand  this  difference  between  the  things  the 
more  clearly  we  can  define  the  word.  Hence  we  shall  stop 
speaking  about  words  for  a  little  and  speak  about  the  prin- 
ciples of  Division  or  Classification.  At  the  end  of  the 
chapter  we  shall  return  to  the  discussion  of  words  and  their 
interpretation. 

When  we  have  made  two  classes  to  one  or  other  of  which 
every  object  in  the  world    can   be    assigned   ac-   pj.^^^ 
cording  as  it  has  or  has  not  some  given  quality  or   of  division 
relation,  each  of  these  classes  can  be  subdivided  subdivision, 
with  reference  to  some  other  quality. or  relation;    and  this 

45 


46  DIVISION   AND   CLASSIFICATION. 

process  can  be  carried   on  indefinitely,  as  in  the  following 
table. 

Substances 

I 


Corporeal  =  Bodies  Incorporeal 

I 

I  i 

Living  =  Organisms  Inanimate 

I  I 

Capable  of  feeling  =  Animals  Incapable  of  feeling  =  Plants 


i  I 

Rational  =  Man  Irrational  =  Lower  Animals 

I 


Etc.  Etc. 

This  division  and  subdivision  of  everything  into  precisely 
two  classes  according  to  the  presence  or  absence  of  some 
given  mark  (technically  called  Division  l>y  Dichotomy^  is 
often  useful,  and  in  the  example  just  given  seems  very  ap- 
propriate, but  there  are  cases  in  which  it  is  cumbersome  and 
rather  absurd,  e.g.: 

Colored  Objects 


Red  Not  Red 


I  I 

Orange  Not  Orange 

I 


I  I 

Yellow  Not  Yellow 


1 

Green 

Not 
1 

I 
Green 

Etc. 

Etc. 

In  this  case  it  would  be  better  for  almost  every  practical 
purpose  to  divide  directly  into  Red,  Orange,  Yellow,  Green, 
and  the  other  colors.  Hence  instead  of  dividing  according 


CROSS-DIVISION.  47 

to  the  presence  or  absence  of  some  given  quality  (e.g. ,  red- 
ness), we  may  divide  according  to  the  determination  in  some 
given  respect  (e.g.,  color),  making  as  many  co-ordinate  classes 
as  there  are  different  determinations  in  that  respect;  and 
then  we  can  proceed  to  subdivision,  with  reference  to  other 
respects,  if  such  subdivision  is  necessary,  immediately  and 
without  so  much  confusion. 

Colored  Objects 


I  !  II 

Red  Orange  Yellow  Green,  etc. 


I          I  I 

Light     Dark     Light     Dark 

Whether  each  class  should  or  should  not  be  subdivided  in 
the  same  respect  as  every  other  (eg.,  each  color  into  light 
and  dark),  depends  altogether  upon  the  purpose  of  the  divi- 
sion. Often  it  is  impossible.  Creatures  with  a  nervous 
system,  for  example,  could  be  divided  according  to  its 
arrangement  or  development.  Those  without  one  could 
not. 

The  one  great  rule  for  division  is  that  each  of  ihe  objects 
divided  shall  have  one  place  in  the  system,  and  only  one.  Thus, 
if  \ve  should  divide  all  human  beings  into  Americans,  Europe- 
ans, and  uncivilized  peoples,  we  should  commit  a  double 
blunder,  for  some  peoples,  such  as  the  Japanese,  would  not 
fall  under  any  head,  and  some  of  the  American  Indians  would 
fall  under  two. 

When  any  object  falls  into  each  of  two  co-ordinate  classes — 
as   in    this    example — there  is  said  to  be  a    Cross-division. 
This  is  always  likely  to  occur   when    u'e    classify    objects  in 
more  than  one  respect  at  a  time.     If  we  had  first   Cross_ 
divided  peoples  according  to   their  geographical   division- 
distribution  and  afterwards  subdivided  each  group  according 
to    their    civilization,    or    vice    versa,    this    could    not    have 
occurred,  e.g., 


DIVISION   AND   CLASSIFICATION. 


I.  American  • 

A.  Civilized 
B.  Uncivilized  < 

w 
X  * 

II.  European    • 

A.  Civilized 
B.  Uncivilized 

o 

w 

A, 

(  A.  Civilized 
III.  Asiatic        -{  r>    TT     •   -r     A 
\  B.  Uncivilized 

„,,    .  ,.  .              f  A.  Civilized 
IV.  African       <  0    TT      .   .,.      , 
j  B.  Uncivilized 

V.  Australian  - 

A.  Civilized 
B.  Uncivilized 

VT      Other       f  A.  Civilized 

'  islanders     j  B.  Uncivilized 

i.  Savage 


2.  Barbarous 


(a. 
Ib. 

a. 

b. 

c. 
Id- 


To  be  sure,  the  uncivilized  Indians  still  fall  into  two 
classes,  Americans  and  uncivilized  Americans,  but  this  is 
now  perfectly  proper,  because  the  classes  are  no  longer 
co-ordinate  ;  the  latter  is  subordinate  to  the  former. 

Cross-division  is  a  particularly  bad  logical  blunder,  because 
of  the  mental  confusion  which  is  shown  by  the  indiscriminate 
use  of  several  principles  of  classification  (technically  called 
Fundamenta  Divisionis)  at  once. 

"Overlapping,  however,  may  be  unavoidable  in  practice, 
owing  to  the  nature  of  the  objects.  There  may  be  objects 
in  which  the  dividing  characters  are  not  distinctly  marked, 
objects  that  possess  the  differentiae  of  more  than  one  group 
in  a  greater  or  less  degree.  Things  are  not  always  marked 
off  from  one  another  by  hard  and  fast  lines.  They  shade 
into  each  other  by  imperceptible  gradations.  A  clear  separa- 
tion of  them  may  be  impossible.  In  that  case  you  may 
allow  a  certain  indeterminate  margin  between  your  classes, 
and  sometimes  it  maybe  necessary  to  put  an  object  into  more 
than  one  class."  * 

*  Minto's  "  Logic/'  p.  95. 


CROSS-DIVISION. 


49 


Cross-division  should  be  distinguished  from  cross-refer- 
ences, such  as  one  finds  in  the  subject-catalogues  of  libraries. 
If  one  does  not  know  whether  to  put  a  book  on  the  history  of 
English  philosophy  under  'History'  or  'England'  or 
'Philosophy',  he  can  solve  the  question  practically  by 
putting  it  under  one  of  them,  say  'England',  and  then 
saying  under  each  of  the  other  heads  '  See  also  England  '. 

The  blunder  of  dividing  in  such  a  way  as  to  leave  out  alto- 
gether some  object  that  ought  to  have  been  included  is  likely 
to  be  the  result  of  haste  rather  than  of  confusion.  Where  one 
knows  all  the  objects  that  are  to  be  divided,  he  must  look 
about  carefully  to  see  that  none  are  omitted.  Where  he  does 
not  he  must  leave  room  in  his  scheme  of  division  and  subdi- 
vision for  additions,  e.g. : 


in 

w 
0 

I. 

Indo-European    -< 

o 

55 

II. 

Semitic 

III. 

Turanean 

IV. 

Others  ? 

A. 

Slavonic 

]'• 

I    2. 

Russian 
Others? 

B. 

Grasco-Roman 

C. 

Celtic 

f1' 

English 

I). 

Teutonic 

i 

German 
Dutch 

I  4. 

Others  ? 

E. 

Others? 

It  need  hardly  be  added  that  a  surbordinate  class  should 
not  contain  any  objects  not  included  in  the  class  above  it. 
If  we  are  classifying  serious  works  of  history  it  would  not  do 
to  include  Dumas'  "Three  Musketeers  "  in  one  of  the  subdi- 
visions, even  though  it  contains  some  historical  matter,  for  it 
is  not  a  serious  work  of  history. 

Students  should  make  themselves  familiar  with  the  follow- 
ing names  :  Genus  is  the  name,  of  a  class  of  objects  divided 
into  smaller  classes.  Each  of  these  smaller  classes  is  called  a 
Species.  Where  there  is  a  system  of  divisions  and  subdivisions 


SO  DIVISION    AND    CLASSIFICATION. 

any  class  is  called  a  species  with  reference  to  those  above 
it,  a  genus  with  reference  to  those  below  it,  e.g. , 
organisms  or  living  bodies  are  a  'species'  of 
bodies,  but  are  a  'genus'  of  which  animals  are 
a  species.  In  such  a  system  the  highest  class  of  all  is  called 
the  Summum  Genus  ;  the  lowest,  the  Infirna  Species.  ' '  When 
a  thing  is  so  peculiar  and  unlike  other  things  that  it  cannot 
easily  be  brought  into  one  class  with  them,  it  is  said  to  be 
sui  generis,  or  of  its  own  genus";*  e.g.,  the  rings  around 
Saturn  amongst  heavenly  bodies,  the  ornithorhyncus  and 
amphioxus  amongst  animals.  The  qualities  peculiar  to  the 
members  of  some  one  species  or  genus,  and  in  virtue  of  which 
that  species  or  genus  is  distinguished  from  other  species  or 
genera,  are  called  the  Differentice  of  the  species  or  genus. 
Thus  the  possession  of  reason,  by  which  men  may  be  dis- 
tinguished from  the  lower  animals,  can  be  called  the  differ- 
entia of  the  human  species.  Qualities  peculiar  to  a  species, 
but  not  used  in  defining  it  or  distinguishing  it  from  other 
species,  are  called  Properties,  or  Prnpria.  Thus  laughter  is 
a  proprium  of  human  beings.  Qualities  or  states  not  char- 
acteristic of  a  species  are  called  Accidents. 

So  far   we   have   taken  up    the  purely  formal   or  negative 

aspect  of  divi>ion,  and  pointed   out  the  blunders  which  any 

system    of   division     should     avoid.       But    every 

classified-       actual  system  of  division   lias  a   purpose,  and  to 

tion  and  its      attain  a  purpose  it  is  necessary  to   move  in  some 

definite  direction,  not  merely  to  avoid  the  pitfalls 

on  the  road.      A  scientific  classification  is  nothing  more  than 

a  system  of  division  carried  out  in  such  a  way  as  to  best  serve 

a  given  purpose. 

One  purpose  served  by  classification  is  to  enable  a  person 
to  find  any  given  object  with  the  least  possible  trouble.  If  I 
have  only  two  or  three  dozen  books  it  is  not  worth  while  to 
arrange  them  on  the  shelf  in  any  particular  order,  for  I  can 

*  Jevons. 


SCIENTIFIC   CLASSIFICATION   AND   ITS   PURPOSES.    51 

always  find  the  one  I  want  at  a  single  glance.  But  if  I  have 
a  library  full  of  books  and  pamphlets,  and  I  want  to  be  sure 
of  finding  one  of  them  at  a  moment's  notice,  I  must  arrange 
them  alphabetically,  or  topically,  or  in  some  other  fixed 
order.  When  the  things  themselves  cannot  be  arranged 
according  to  any  plan,  the  next  best  thing  is  to  arrange  their 
names  in  some  fixed  order — usually  alphabetical— and  after 
the  name  write  where  the  thing  is  to  be  found.  In  this  way 
we  construct  directories  and  gazetteers  and  the  indexes  of 
books. 

A  second  purpose  served  by  classification  is  to  give  an 
easy  means  of  identifying  an  object  when  it  is  found.  A 
suspicious  looking  person  is  arrested  by  the  police  and  they 
wonder  who  he  is  ;  so  they  turn  up  their  classified  list  of 
criminals,  looking  up  (say)  the  class  '  Eyes,  blue  '  ;  then  the 
subdivision  '  Height,  five  feet  eleven  inches '  ;  then  the 
further  subdivision  'Fingers,  tapering';  and  so  on,  till  at 
last  they  find  the  photograph  or  thumb-mark  of  the  individual 
in  question  with  his  name  and  record.  If  the  descriptions 
were  not  classified  the  work  of  identifying  the  man  might  be 
endless. 

A  function  similar  to  these  two,  yet  distinguishable  from 
them,  is  to  enable  us  to  find  or  identify  a  given  kind  of  object. 
Often  we  do  not  know  what  book  or  man  we  want  to  find, 
but  the  classified  list  can  tell  us.  We  want  some  book  or 
other  about  colonial  furniture,  and  the  subject-catalogue 
names  several  ;  we  want  a  man  who  can  mend  china,  and 
the  classified  list  of  tradesmen  at  the  end  of  the  city  directory 
gives  a  number  of  names  and  addresses.  In  the  same  way  if 
we  find  a  new  kind  of  plant  in  the  woods  and  want  to  know 
what  it  is,  we  use  some  botanical  '  key,'  in  which  kinds  of 
plants  are  identified  by  a  series  of  obvious  characteristics, 
and  discover  the  name  (not  of  that  individual  as  such,  but) 
of  that  kind  of  plant.  In  the  same  way  also  a  classified  list 
of  symptoms  might  save  a  young  physician  much  valuable 
time  in  diagnosing  a  disease. 


52  DIVISION   AND   CLASSIFICATION. 

A  fourth  object  of  classification  is  to  make  it  easy  to  deal 
at  the  same  time  with  tilings  that  bear  any  special  relation  to 
each  other.  To  this  end  we  put  the  things  themselves  or 
their  names  together.  A  grocer  puts  in  the  same  basket  all 
the  parcels  that  are  to  go  to  the  same  house  ;  a  lady  writes  on 
the  same  list  the  names  of  the  people  or  shops  to  be  visited 
on  the  same  afternoon.  Here  the  classification  is  made  for 
an  immediate  practical  purpose — something  must  be  done 
about  each  of  the  people  or  things  in  question,  and  the  class- 
ified list  helps  us  to  do  it.  But  often,  and  this  is  the  object 
of  classification  in  science,  things  or  the  names  of  things  are 
put  together  because  it  is  desirable  to  think  of  them  not  only 
at  the  same  time  but  in  relation  to  each  other.*  Thus  chrono- 
logical tables,  maps,  and  astronomical  charts  are  made  not 
only  to  show  what  happened  in  a  given  year  or  the  location 
of  a  given  place,  but  also  to  show  the  general  sequence  of 
events  at  any  given  period,  the  general  conformation  of  a 
country,  the  general  arrangement  of  a  planetary  system.  In 
these  cases  the  relations  that  determine  the  classification  are 
those  of  time  and  space,  but  they  may  be  anything  :  degree 
of  scholarship,  in  arranging  a  list  of  students;  degree  of 
strength,  in  a  list  of  acids  ;  durability,  in  a  list  of  fabrics  or 
dyes  ;  cause  and  effect,  when  the  writer  on  medicine  puts  to- 
gether all  the  causes  and  symptoms  of  a  given  disease  ; 
means  and  end,  when  he  adds  a  list  of  remedies. 

Scientific  classifications  are  most  concerned  with  relations  of 
resemblance  and  contrast.      When  a  naturalist,  for  example, 

*  Tt  is  rather  common  to  speak  as  though  all  classification  were  of 
one's  ideas  or  concepts  of  things,  but  this  is  a  blunder.  A  psychologist 
classifies  ideas  and  feelings  when  he  points  out  their  resemblances  and 
differences  ;  e.g.,  the  difference  between  a  feeling  of  terror  and  a 
feeling  of  contempt  ;  but  a  naturalist  classifies  things.  J  It  is  the  business 
of  a  psychologist  to  observe  the  difference  between  thoughts  as  such; 
but  every  other  scientist  is  concerned  with  the  difference  between  the 
objects  that  we  think  of,  not  the  thoughts  themselves,  j  To  think  of  the 
difference  between  things  is  not  the  same  as  to  have  different  thoughts  of 
them. 


SCIENTIFIC   CLASSIFICATION   AND   ITS   PURPOSES.     53 

classifies  all  animals  into  vertebrates  and  non-vertebrates,  he 
merely  asserts  that  each  of  a  certain  long  list  of  animals  has 
a  backbone,  and  in  this  respect  and  certain  others  that  fol- 
low from  it  resembles  each  of  the  others  and  differs  from  all 
of  those  not  on  the  list. 

But  what  points  of  resemblance  and  contrast  must  be  re- 
garded, and  in  what  order,  if  we  are  to  make  a  classification 
scientific?  The  answer  to  this  is  that  no  basis  of  classifica- 
tion— wo  fundamentum  divisionis — is  any  better  than  any  other 
in  itself.  The  only  general  rule  is  to  choose  and  arrange 
fundamenta  dwisionis  in  the  way  that  best  shows  the  points  of 
resemblance  and  contrast  in  which  we  are  interested  or  likely 
to  be  interested.  It  is  just  as  scientific  to  classify  books  by 
their  size,  publishers,  date,  color,  type,  or  language  as  by 
their  author  or  subject-matter,  and  a  great  deal  more  so  if 
we  are  interested  in  the  former  and  not  in  the  latter. 

If  we  are  not  interested  in  any  special  characteristic  of  the 
objects  classified  the  only  thing  left  is  to  try  to  get  into  the 
same  class  objects  that  have  a  great  many  things  in  common 
and  into  different  classes  objects  that  have  very  little  in  com- 
mon, so  "  that  we  shall  be  enabled  to  make  a  maximum 
amount  of  aggregate  assertion  with  a  minimum  number  of 
propositions."*  To  do  this  -we  nm;;t  choose  as  our  first 
fundamentum  divisionis  that  point  on  which  the  greatest  num- 
ber of  other  noteworthy  points  of  difference  depend.  It  is 
better  to  divide  all  living  things  into  animals  and  plants  than 
into  those  which  weigh  more  than  a  pound  and  those  which 
weigh  less ;  because  the  possession  of  sensation  and  the 
power  of  spontaneous  motion  •)-  which  distinguish  animals 
from  plants  involve  innumerable  other  points  of  difference, 
while  the  size  involves  little  or  nothing  more  :  to  say  that  a 

*  Venn's  "Empirical  Ix)gic,"  Chap.  XIII.,  to  which  the  reader  is 
referred.  (Macmillan.) 

•j-  This  of  course  is  the  popular  distinction.  If  we  wish  to  be  more 
scientific  we  should  say  'the  fact  that  they  require  protoplasmic  food- 
stuff, or  cannot  decompose  carbonic  acid  gas,  which  distinguishes,'  etc. 


54  DIVISION   AND   CLASSIFICATION. 

thing  is  a  plant  tells  a  great  deal   about  it  ;  to  say  that   it 
weighs  less  than  a  pound  tells  hardly  anything. 

It  is  this  principle  of  trying  to  get  into  the  same  class 
those  objects  which  on  the  whole  are  most  alike  that  prevails 
in  the  classification  of  animals  and  plants  in  natural  history 
and  of  books  in  the  subject-catalogues  of  libraries. 

Any  system  of  classification  that  regards  general  resem- 
blance is  liable  to  be  upset  by  an  advance  in  knowledge  or  a  / 
change  in  scientific  interests.  The  common  man  calls  a  / 
whale  a  fish,  the  zoologist  says  it  is  not  a  fish  b^t  a  mammal,"4 
because  he  has  found  out  that  on  the  whole  living  in  the  sea 
and  looking  like  a  fish  involves  fewer  other  noteworthy 
characteristics  than  suckling  the  young.  In  Dewey's  Library 
Index  illusions  are  classified  with  witchcraft  and  fraud  because 
they  involve  deception,  and  for  the  general  reader  this  is 
perhaps  the  best  classification  ;  but  a  psychologist  would  clas- 
sify illusions  along  with  ordinary  perceptions,  because  both  are 
interpretations  of  sensations  made  in  precisely  the  same  way, 
and  he  knows  that  the  correctness  or  incorrectness  of  the 
interpretation,  which  strikes  the  layman  and  upon  which 
Dewey's  classification  depends,  is  a  mere  accident  and  does 
not  involve  any  further  differences  in  the  mental  processes. 
To  illustrate  the  influence  of  wider  knowledge  or  deeper 
insight  upon  a  whole  system  of  classification  it  is  only  neces- 
sary to  point  out  how  the  old  hard  and  fast  lines  between 
genera  and  species  in  natural  history  have  been  wiped  out  by 
the  theory  of  evolution,  which  shows  how  new  species  are 
being  created  continually  though  slowly  by  the  inheritance 
and  consequent  accumulation  of  a  vast  number  of  small  indi- 
vidual variations. 

The  fact  that  a  system  of  classification  is  likely  to  be  upset 
by  wider  knowledge  is  no  reason  why  it  should  not  be  con- 
structed, for  a  bad  classification  is  better  than  confusion  ;  and 
however  bad  it  may  be,  it  is  likely  to  contribute  something 
toward  the  attainment  of  the  wider  knowledge  by  which  it 
can  be  corrected. 


NAMING.  5  5 

When  a  classification  has  been  made,  the  resemblances 
and  differences  which  it  indicates  can  be  still  further  marked 
and  more  easily  remembered  and  talked  about  by  lUmins;. 
the  use  of  class  names.  The  words  vertebrate,  mammal,  radi- 
ate, batrachian  are  all  scientific  terms  invented  for  this  pur- 
pose. But  the  use  of  class  names  was  not  invented  by  scien- 
tists, for  every  common  name  marks  out  a  class  of  things 
which  it  serves  to  distinguish  from  all  others.  Animals  and 
plants,  trees  and  grasses,  hawks  and  doves,  were  distinguished 
and  contrasted  long  before  science  existed.  /  The  scientist, 
as  Venn  says,  usually  finds  the  highest  ami  lowest  classes 
of  things  already  made  and  named.  His  business  is  only 
to  state  their  most  important  differences  distinctly  (which 
sometimes  involves  a  correction  in  the  classification  of  an 
ambiguous  kind,  such  as  the  whale)  and  to  arrange  the  inter- 
mediate groups. 


CHAPTER  V. 

THE   USES   OF   SINGLE  WORDS   AND   PHRASES. 

We  have  seen  already  how  to  avoid  certain  gross  blunders 
which  result  from  the  ambiguity  or  misinterpretation  of  words 
and  statements  ;  but  if  we  are  to  acquire  any  fine  discrim- 
ination in  the  interpretation  and  use  of  language  our  study  of 
words  and  sentences  must  not  end  here.  Hence  several 
chapters  more  must  be  devoted  to  them. 

To  understand  the  exact  meaning  of  a  word  in  any  partic- 
ular sentence  it  is  not  enough  to  know  its  definition  ;  for 
however  unambiguous  the  meaning  of  a  word  may  be  as  given 
in  a  dictionary  it  may  be  used  for  any  one  of  several  different 
purposes,  and  if  we  do  not  understand  the  differences  between 
these  purposes  we  cannot  be  sure  of  interpreting  the  word 
aright. 

Wilh  reference  to  each  one  of  these  different  purposes 
words  are  divided  into  different  classes — usually  two  ;  but 
since  the  same  word  can  be  classified  with  reference  to  differ- 
ent purposes  it  can  belong  to  as  many  different  classes  as  there 
are  purposes  with  reference  to  which  it  can  be  classified. 
\Ye  shall  see,  however,  that  not  every  word  can  be  classified 
with  reference  to  all  these  different  purposes. 

The  first  division  of  words  which  we  shall  consider  is  into 
Terms.  those  that  are  '  Terms',  and  those  that  are  not. 

A  term  is  a  word  or  group  of  words  used  to  indicate  or 
identify  the  objects  about  which  a  person  speaks,  or  the 
states,  qualities,  actions  or  other  relations  whose  possession  by 

56 


TERMS.  5  7 

an  object  is  under  consideration.  It  is,  in  brief,  a  name  in 
the  broadest  sense  of  the  word.  In  the  sentence  '  The  pres- 
ent Emperor  of  Germany  is  remarkab,b/_^ucrgetic  '  the  first 
five  words  are  regarded  as  a  single  term  because  they  are  used 
together  to  point  out  the  individual  under  discussion  ;  and 
because  the  last  two  words  of  the  sentence  are  used  together 
to  indicate  a  single  quality,  they  also  are  regarded  as  a  single 
term.  In  other  connections,  of  course,  the  words  Emperor, 
Germany,  energetic,  would  be  regarded  as  separate  terms, 
e.g. ,  The  Emperor  is  energetic  ;  Germany  is  a  beautiful  coun- 
try. Even  in  the  case  of  the  sentence  given,  if  \ve  should  be 
asked  to  '  define  our  terms  '  it  would  be  proper  enough  to 
take  up  the  words  separately,  as  they  might  appear  elsewhere, 
and  explain  that  by  '  remarkably  '  was  meant,  not  '  exces- 
sively', but  'noticeably';  by  'energetic',  not  'meddle- 
some' but  vigorous'.  But  if  we  wished  to  be  absolutely 
accurate,  though  tedious,  we  should  add  to  our  explanation  of 
the  meaning  of  the  separate  words  an  explanation  of  the  phrase 
or  term  as  a  whole. 

Though  every  term  is  a  word  or  ccmbination  cf  words, 
the  structure  of  language  is  such  that  some  words  can  never 
be  used  as  complete  terms.  The  object  of  thought  is  indi- 
cated y  the  subject  of  a  sentence  ;  its  relations  under  dis- 
cussion, by  the  predicate.  Such  words  as  prepositions,  con- 
junctions and  adverbs  cannot  be  either  subjects  or  predicates 
and  therefore  they  cannot  be  terms,  though  they  can  be  parts 
of  terms.  We  cannot  say,  for  example  :  Of  is  energetic  ; 
•nevertheless  is  very;  etc.  We  can  say  '  of  is  a  preposition  ; 
but  then  the  word  is  used  as  a  noun  and  is  not  taken  in  its 
ordinary  sense.  Unless  a  relation  is  discussed — affirmed, 
denied,  or  questioned — the  word  that  indicates  it  is  not  a 
term.  The  word  'of  in  the  phrase  'The  Emperor  of  Ger- 
many' indicates  a  relation,  but  it  is  not  a  term,  because 
nothing  is  said  about  the  relation  it  indicates.  It  merely 
forms  a  part  of  the  description  of  the  object  some  other  of 
whose  relations  is  discussed.  Prepositions  joining  nouns  to 


58        THE  USES   OF  SINGLE   WORDS   AND   PHRASES. 

each  other,  and  possessive  cases  are  always  devoted  to  the  ex- 
pression of  relations  which  are  involved  in  the  conception  of 
an  object  but  not  discussed.  For  that  reason  they  can  never 
be  terms.  On  the  same  principle,  adjectives  are  true  terms 
when  they  follow  the  verb  'to  be '  or  its  equivalents  as 
predicates,  e.g.,  in  the  sentence  '  The  horse  is  white',  but 
not  when  they  are  in  their  usual  position,  as  in  the  sentence 
'  The  white  horse  kicks'. 

Words  which  can  be  used  as  complete  terms  are  called 
Categorematic  (Greek,  Karrfyopecd,  to  assert);  those  which 
can  not,  and  which  therefore  can  not  be  used  except  when 
they  are  combined  into  a  term  with  others,  are  called  Syn- 
categorematic  (Greek,  &vv,  together  with,  andKaTTjyopeoo'). 

The  distinctions  which  we  have  to  discuss  in  the  rest  of 
this  chapter  all  have  reference  to  terms.  We  shall  therefore 
have  nothing  more  to  say  at  present  about  syncategorematic 
words. 

The  first  distinction  to  be  made  with  reference  to  terms 
is  between  those  which  are  used  demonstratively  and  those 

which    are    used    descriptively.       By  a    Demon- 
Demonstra-  .  ,  . 

tive  and  strative  term  is  meant  one  that  points  out  an  ob- 
ject ;  by  a  Descriptive  term,  one  that  tells  some- 
thing about  it.  When  we  say  '  John  is  angry '  or  '  That  is 
very  beautiful',  the  words  'John'  and  'that'  are  used 
demonstratively  and  the  remainder  of  the  sentences  are 
intended  to  describe  the  objects  that  they  point  out./  The 
word  '  John  '  is  of  course  a  proper  name  and  the  word  'Sthat ' 
a  '  4emonstrative  '  pronoun.  These  parts  of  speech  are  de- 
voted so  exclusively  to  pointing  objects  out,  and  adjectival 
phrases  like  '  angry  '  and  '  very  beautiful '  are  devoted  so  ex- 
clusively to  their  description  that  if  the  order  of  the  sentences 
were  reversed  and  we  said  '  Angry  is  John  '  or  '  Very  beauti- 
ful is  that ',  it  would  still  be  plain  which  words  were  used  to 
point  out  the  objects  under  discussion,  and  which  were  used 
to  describe  them. 

In   the  examples  just  given  the  subject  of  each  sentence 


DEMONSTRATIVE   AND   DESCRIPTIVE.  59 

was  demonstrative  and  the  predicate  descriptive,  and  by 
straining  matters  a  little  we  can  say  that  this  is  always  so. 
We  can  say,  for  example,  that  in  the  propositions  '  A  is 
larger  than  B  ',  '  A  is  bullying  B  ',  everything  but  the  subject 
'  A '  is  part  of  a  predicate  whose  function  is  merely  to  de- 
scribe or  tell  something  about  A.  This,  I  suppose,  would  be 
the  grammarian's  interpretation  of  the  sentences,  and  it  is 
the  interpretation  that  we  assumed  when  we  defined  the  sub- 
ject of  a  sentence  as  the  name  of  the  object  about  which  we 
are  speaking.  But  it  is  not  quite  fair,  for  in  each  of  these 
sentences  we  tell  quite  as  much  about  B  as  about  A.  The 
fairer  way  is  to  regard  the  sentence  as  made  up,  not  of  two 
parts,  a  subject  and  a  predicate,  but  of  three  :  two  demon- 
strative terms,  and  a  third  term  that  describes  some  relation 
between  the  things  which  they  point  out.  In  view  of  this 
interpretation  of  propositions  like  these  we  cannot  say  that  a 
predicate  is  always  descriptive  (or  even  that  it  always  con- 
sists of  a  single  term).  But  there  is  nothing  in  what  we  have 
said  to  prevent  us  from  saying  that  the  subject  is  always  de- 
monstrative. If  we  do  say  so,  however,  we  must  make  it  plain 
that  we  are  speaking  of  real  subjects  and  not  such  nominal 
subjects  as  '  it '  and  '  there  '  in  propositions  like  these  :  '  It 
is  a  long  distance  from  A  to  B ' ;  '  It  is  a  long  road  that  knows 
no  turning';  '  There  is  a  lion  in  the  way'.  Sometimes,  more- 
over, it  is  hard  to  tell  what  is  the  real  subject.  In  this  last 
proposition,  for  example,  are  we  telling  about  the  lion,  as  the 
form  of  the  sentence  seems  to  imply,  or  are  we  telling  about 
the  way  and  why  we  cannot  travel  in  it  ? 

Nouns  (i.e.,  nouns  substantive)  are  usually  used  demon- 
stratively ;  but  they  can  also  be  used  descriptively.  When 
we  say  '  A  man  came  to  the  house  ',  the  term  '  a  man  '  is  de- 
monstrative, for  it  points  out,  rather  indefinitely  to  be  sure, 
who  it  was  that  came ;  but  when  we  say  '  John  is  a  man  ',  the 
term  is  used  descriptively,  for  it  is  intended  to  summarize 
a  great  many  of  John's  attributes,  to  indicate  his  general  re- 
semblance to  the  other  creatures  we  call  men,  and  perhaps 


60        THE   USES   OF   SINGLE   WORDS   AND  PHRASES. 

to  convey  an  idea  of  his  biological  relations  to  them  and  to 
other  animals. 

Since  it  is  possible  to  identify  an  object  more  or  less  defi- 
nitely by  describing  it,  a  term  whose  primary  function  in  a 

given  sentence  is  to  do  the  one  often  serves  at 
Connotative     '  ....          .,  .      , 

and  non-  the  same  time  incidentally  to  do  the  other.  \\  hen 
connotative.  ^,  , 

we  say  that  a  man  came  to  the  house  we  not  only 

tell  the  hearer  that  one  or  other  of  a  certain  large  group  cf 
things  came  to  the  house,  but  we  incidentally  describe  that 
thing,  implying  that  it  has  all  the  qualities  and  other  rela- 
tions of  a  man  ;  and  when  we  say  that  John  is  a  man  we  not 
only  describe  him  but  incidentally  we  tell  that  he  is  one  of  a 
certain  group.  Terms  which  perform  this  double  function 
are  called  Connotative;  those  which  do  not,  Non-connota- 
tive.* 

What  words  really  are  connotative  and  what  non-connota- 
tive,  and  even  the  definition  of  these  terms  themselves,  is  a 
matter  about  which  logicians  are  not  all  agreed  ;  but  the 
distinction  will  be  illustrated  well  enough  for  our  purposes  if 
we  say  that  the  ordinary  Common  Nouns  of  grammar  are 
connotative  (e.g.,  'man',  'horse',  'pig'),  and  that  Proper 
Names  and  Abstract  Nouns  are  probably  not. 

Whether  a  proper  name  is  to  some  extent  descriptive  as 
well  as  demonstrative  depends  altogether  upon  whether  there 
exists  any  convention  in  virtue  of  which  any  particular  name 
i-;  applied  only  to  certain  classes  of  objects.  In  English- 
speaking  countries  nowadays,  for  example,  surnames  usually 
indicate  family  connections.  Elsewhere  and  at  other  times 
they  have  indicated  something  else.  A  Christian  name  may 
be  given  merely  because  a  parent  thinks  it  pretty  ;  and  yet  it 
is  usually  chosen  with  some  reference  to  sex.  Nevertheless 

*  A  '  connotative  '  term,  as  defined  in  logic,  must  not  be  confused  with 
the  somewhat  similar  terms  '  which  have  connotation  '  as  defined  in  books 
of  rhetoric.  They  both  do  something  incidentally;  but  this  incidental 
function  us  described  in  rhetoric  is  generally  some  kind  of  appeal  to 
feeling. 


SINGULAR   AND  GENERAL.  61 

I  doubt  whether  \ve  can  say  that  to  that  extent  it  is  descrip- 
tive, for  however  unusual  and  outrageous  it  might  be  to 
name  an  English  boy  Mary,  one  could  hardly  say  that  the 
parent  who  did  it  had  falsely  asserted  that  the  child  was  a 
girl.  It  need  hardly  be  said  that  when  we  call  some  one  a 
Nero  or  a  Socrates  or  a  Napoleon  these'  proper  names  are  used 
altogether  in  a  descriptive  sense.  \f 

When  a  term  is  used  demonstratively — to  point  out  an  ob- 
ject of  thought — it  is  said  by  logicians  to  be  used  'Denotatively' 
or  in  its  '  Extension  ' ;  when  used  to  describe  one,  it  is  said  to 
be  used  '  Connotatively  '  or  in  its  '  Intension  '.  From  this  it 
follows  that  when  we  define  a  term  we  tell  the  qualities  it  con- 
notes ;  when  we  give  an  example  we  tell  one  of  the  things  it 
denotes.  As  Bosanquet  puts  il:  "The  denotation  of  a  name 
consists  of  the  things  to  which  it  applies,  the  connotation 
consists  of  the  properties  which  it  z'wplies."  * 

Proper  names  are  applied  (more  or  less  arbitrarily)  to  some 
individual  object  for  the  sake  of  indicating  that  particular  ob- 
ject as  distinguished  from  all  others.      But  this  function  can 
also  be  discharged  by  some    descriptive  phrase 
which  is  obviously  applicable  to  only  one  particu-   and 
lar  object  (e.g.,  '  the  man  at  my  right ',  '  my  black 
dog  ').    In  either  case  a  term  which  is  intended  to  discharge  this 
function  is   called  Singular.      A  General  term,   on  the  other 
hand,   is  one  applied   to   every  object  which   possesses  some 
given  characteristic  or  characteristics,  and  used  to  distinguish 
any  object  which   possesses   such  characteristic   or  character- 
istics from  objects  which  do  not  (e.g.,  '  triangle  ',  'angular'). 

Because  a  general  term  is  not  applicable  to  an  object  un- 
less that  object  possesses  a  given  attribute,  it  is  evident  that 
general  terms  are  all  connotative. 

Singular  terms  are  intended  to  distinguish  a  certain  "real 
essence  " ,  as  Locke  would  have  said,  a  certain  person  or  thing 
that  remains  that  same  person  or  that  identical  thing  through- 
out all  the  changes  it  may  undergo.  '  The  thin  black- 

*  The  Essentials  of  Logic,  p.  88. 


62        THE   USES  OF   SINGLE  WORDS   AND   PHRASES. 

haired  man  who  passes  here  every  morning ' — this  phrase  is ' 
a  singular  term,  because  it  is  designed  for  the  purpose  of 
pointing  out  a  special  individual  who  would  remain  the  same 
person  when  the  description  was  no  longer  applicable.  For 
the  purpose  in  hand  any  other  description  might  have  done 
as  well,  for  though  we  may  identify  the  person  by  means  of 
a  description,  it  is  the  person,  not  the  described  characteris- 
tics, that  we  mean.  General  terms  are  intended  to  distin- 
guish what  Locke  would  have  called  "nominal  essences" 
from  each  other.  The  terms  'a  thin  man',  'travellers', 
'  good  students  ',  '  good  ',  '  gas  '  are  each  applicable  to  any 
object  or  set  of  objects  only  so  long  as  the  objects  possess 
the  attributes  indicated  ;  they  are  equally  applicable  to  any 
objects  possessed  of  those  attributes,  and  are  chosen  for  the 
express  purpose  of  calling  attention  to  the  presence  of  the 
attributes. 

Sometimes  the  same  term  may  be  singular  in  one  connec- 
tion (e.g.,  'the  child  is  sick';  '  Ccesar  was  killed'),  and  gen- 
eral in  another  (e.g.,  '  the  child  is  father  to  the  man  ' ;  '  he  is 
a  regular  Cutsar').  Thus  in  logic  it  is  the  meaning  of  a 
word  that  counts,  not  the  outward  form. 

Often  a  descriptive  phrase  whose  primary  purpose  is  to 
identify  an  object  is  not  quite  accurate,  but  if  it  suggests  the 
required  object  this  does  no  harm  so  far  as  the  identification 
is  concerned.  If  I  say  that  the  peddler  who  was  so  impudent 
at  our  door  yesterday  morning  was  afterwards  arrested  on  a 
serious  charge,  and  if  you  recognize  the  man  from  my  descrip- 
tion, the  description  has  answered  its  purpose,  even  though 
it  was  not  yesterday,  but  the  day  before,  that  he  was  at  our 
door.  Sometimes,  however,  a  number  of  descriptive  words 

are  added  to  a  demonstrative  term  when  they  are 
Epithets.  .         .       .  .        ,, 

wholly    unnecessary  lor  the  identification  of  the 

object,  e.g.,  'swift- footed'  Achilles,  '  the  beautiful  and  accom- 
plished '  Miss  Blank,  this  'most  dangerous'  disease.  Such 
epithets  have  a  rhetorical  value,  for  they  convey  in  a  neat  way  a 
desired  conception  of  an  object  about  which  something  is  to  be 


COLLECTIVE   AND   DISTRIBUTIVE.  63 

said  ;  but  no  one  is  logically  justified  in  using  one  of  them  if 
its  applicability  is  a  question  at  issue  or  depends  in  any  way 
upon  one.  A  lawyer,  for  example,  has  no  right  to  refer  to 
a  person  accused  of  rriurder  as  '  this  brutal  assassin  '  until  after 
the  trial  is  over  and/the  accused  is  found  guilty,  and  then  he 
may  not  wish  to.  Such  descriptive  terms  used  in  this  way 
anTcaTTed  Question-begging  Epithets.  They  beg  the  question 
or  take  for  granted  what  is  to  be  proved,  because  they  have 
the  form  and  position  of  descriptive  epithets  used  to  identify 
an  object;  and  these  nearly  always  point  to  qualities  that  are 
obvious  and  admitted.  Question-begging  epithets  are  gener- 
ally intended  to  appeal  to  the  listeners'  emotions  and  make 
them  partisans  instead  of  unprejudiced  judges.  Thus  they 
are  doubly  unfair. 

When  we  consider  terms  from  another  standpoint  we  must 
distinguish  between  those  that  are  called  Collective  (such 

as    'iury',    'army'      'mob',    'herd',    'crew' 

TN        j    i  i_-   i_  11    j  T^-        Collective 

'  crowd  ,  '  heap    )  and  those  which  are  called  Dis-   and  dis- 

,  .,.      ,     ,  .  ,      tributive. 

tnbutive  (such  as  'man  ,  'soldier  ,  'juryman   , 

*  goat ' ).  A  Collective  term  as  distinguished  from  a  Distribu- 
tive is  one  used  to  denote  any  aggregate  of  similar  and 
separable  things  regarded  as  constituting  some  sort  of  tem- 
porary unit.  When  all  notion  of  the  separateness  of  the 
individuals  in  an  aggregate  is  lost,  so  that  the  combined  whole 
is  regarded,  at  least  for  the  moment,  as  a  true  unit,  the  col- 
lective term  which  names  it  become  distributive.  This  is 
most  likely  to  happen  when  we  think  of  several  such  aggre- 
gates, e.g. ,  'There  were  mobs  in  six  cities  at  once  ',  '  He  was 
convicted  by  three  different  juries1 . 

It  is  extremely  important  to  distinguish  between  state- 
ments which  are  intended  to  apply  to  several  things  con- 
sidered as  a  whole  and  those  intended  to  apply  to  each  of  a 
number  of  individuals.  A  jury  as  a  whole  cannot  get  hun- 
gry, though  each  of  its  members  may.  The  words  'and', 
'all',  'many'  are  singularly  ambiguous  in  this  respect. 
It  was  this  ambiguity  that  gave  point  to  the  newsboy's  re- 


64        THE   USES   OF   SINGLE   WORDS   AND   PHRASES. 

mark:  '  Astor  and  I  are  worth  millions.'  'Three  and 
five'  make  eight,  not  severally  but  conjointly,  while  'three 
and  five '  are  odd  numbers  severally  and  not  conjointly. 
'  They  all'  lifted  a  log  conjointly  (cuncii},  and  '  they  all ' 
told  about  it  severally  Conines).  'The  mosquitoes  in  Alaska 
are  so  large  that  many  of  them  weigh  a  pound.'  The  terms 
.severally  and  conjointly  are  often  used  in  legal  documents  to 
indicate  the  distinction  we  are  discussing.  The  most  usual 
terms  in  logic  are  distributively  and  collectively*  ' 

When  we  take  any  of  these  ambiguous  words  collectively 
at  one  stage  of  an  argument  and  distributively  at  another,  it 

is   possible  to  draw  conclusions  which  a  fair  and 
The  danger.  .  .  _     , 

unambiguous  interpretation  of  the   words  would 

not  warrant,  e.g.,  '  All  the  angles  of  a  plane  triangle  are 
equal  to  two  right  angles  ;  this  is  one  of  them  ;  therefore 
this  angle  is  equal  to  two  right  angles.'  l  All  the  feathers  in 
a  bed  are  extremely  light  ;  the  bed  is  made  up  of  all  the 
feathers  ;  therefore  the  bed  is  extremely  light.'  In  the  first 
of  these  examples  the  word  '  all  '  is  taken  collectively  when 
the  premise  is  admitted,  but  distributively  when  it  is  used  to 
prove  the  conclusion,  and  the  fallacy  is  called  one  of  Di- 
vision. In  the  second  example  the  word  'all'  is  taken  dis- 
tributively in  the  ambiguous  premise  when  it  is  admitted, 
but  collectively  when  the  premise  is  used  to  prove  the  con- 
clusion, and  the  fallacy  is  called  one  of  Composition.! 

*  Both  Jevons  and  Minto  contrast  Collective  terms  with  General  terms. 
Jevons  says  "  We  must  carefully  avoid  any  confusion  between  general 
and  collective  terms  "  (p.  19 >  ;  and  Minto  speaks  of  "  Collective  names 
as  distinguished  from  general  names"  (Logic,  p.  58).  In  each  case, 
however,  it  seems  to  be  an  oversight,  for  in  the  exercise  at  the  end  of  (lie 
chapter  Jevons  says  the  reader  is  to  determine  whether  a  term  is  "collec- 
tive or  distributive  ",  not  collective  or  general.  So  with  Minto,  most  col- 
lective names  fall  under  his  definition  of  general  names  (see  p.  44). 

A  collective  term  may  be  either  singular  or  general,  e.g. :  7'h?  Smiths 
have  a  new  house  (singular)  ;  he  was  attacked  by  a  mob  (general). 

f  A  good  many  fallacies,  such  as  the  stock  argument  for  protective 
tariffs,  are  credited  by  Whately,  Jevons,  and  others  to  this  confusion, 


ABSTRACT    AND   CONCRETE.  65 

A  more  serious  danger  than  that  just  mentioned  is  that 
when  we  use  collective  terms  we  shall  forget  that  the  indi- 
viduals in  the  group  are  not  a  real  unit,  but  can  be  consid- 
ered as  one  for  certain  purposes  only.  I  give  one  example 
of  this  fallacy  here.  There  will  be  others  in  a  later 
chapter. 

"  During  the  last  ten  years  I  have  read  a  great  many- 
books  and  articles,  especially  by  German  writers,  in  which 
an  attempt  has  been  made  to  set  up  '  the  State  '  as  an  entity 
having  conscience,  power,  and  will,  sublimated  above  human 
limitations,  and  as  constituting  a  tutelary  genius  over  us  all. 
I  have  never  been  able  to  find  in  history  or  experience  any- 
thing to  fit  this  conception.  .  .  .  My  notion  of  the  State 
has  dwindled  with  growing  experience  of  life.  As  an  ab- 
straction, the  Stale  is  to  me  only  All-of-us.  In  practice — 
that  is,  when  it  exercises  will  or  adopts  a  line  of  action — it  is 
only  a  little  group  of  men  chosen  in  a  very  haphazard  way  by 
the  majority  of  us  to  perform  certain  services  for  all  of  us. 
The  majority  do  not  go  about  their  selection  very  rationally, 
and  they  are  almost  always  disappointed  by  the  results  of 
their  o\vn  operation.  Hence  'the  State  ',  instead  of  offering- 
resources  of  wisdom,  right  reason,  and  pure  moral  sense  be- 
yond what  the  average  of  us  possess,  generally  offers  much 
less  of  all  those  things."  * 

From  another  standpoint  terms  are  divided  into  'Abstract 
(such  as  'redness',  'anger',  'kindness')  and  Concrete 

(such  as    'red',    'angry   man',     'kind').      Ab- 

Abstract 
stract  terms  are  nouns  used  to  indicate  the  quail-    and 

ties,    states,   acts,  or    other    relations    of   things. 
They  are  'Abstract'  because,   unlike  adjectives    and  verbs, 
they  can  be  used  grammatically  without  any  mention  of  the 
thing  to  which  the  qualities  and  so  forth  belong  and  without 


when,  so  far  as  I  can  see,  they  have  absolutely  nothing  to  do  with  it.     I 
have  treated  of  them  elsewhere. 

*  Sunnier,  "What  Social  Classes  Owe  to  Each  Other",  pp.  9,  10. 


66        THE   USES  OF   SINGLE  WORDS   AND   PHRASES. 

which  these  latter  could  not  exist.  We  can  say,  '  Anger  is 
foolish',  or  '  A  man  is  foolish  to  be  angry  ',  but  not  '  Angry 
is  foolish'.  Abstract  terms  thus  seem  to  'abstract*  or  draw 
away  one's  thought  from  things. 

Every  term  which  is  not  abstract  is  called  Concrete.  Con- 
crete terms  are  therefore  (i)  the  names  of  things,  or  (2) 
adjectives  or  verbs,  that  is  to  say,  names  of  relations  which 
cannot  be  used  grammatically  without  any  mention  of  the 
thing  to  which  they  belong.* 

The  value  of  abstract  terms  lies  in  the  fact  that  through 
their  use  attention  can  be  called  more  briefly  and  more  effect- 
ively than  in  any  other  way  to  certain  features  of  things 
which  we  wish  to  discuss  without  any  special  reference  to  the 
things  themselves.  It  is  easier,  and  on  the  whole  more  effec- 
tive, to  say  'Self-sacrifice  deserves  gratitude'  than  to  say 
'  When  a  person  acts  in  such  a  way  as  to  injure  himself  because 
he  wishes  to  benefit  some  one  else,  the  person  whom  he  meant 
to  benefit  ought  to  feel  grateful,  no  matter  who  the  persons 
may  be'.  But  in  spite  of  the  great  value  of  abstract  terms, 
there  is  no  more  important  practical  rule  in  logic  than  that 
which  says  Beware  of  abstractions  ! 

The  danger  involved  in  the  use  of  abstract  terms  is  due  to 
the  fact  that  such  terms  are  always  nouns  and  that  nouns  are 

usually  the  names  of  things.      We  are  therefore 
Hyposta- 

tising  very  prone  to  regard   the  quality  or  relation  re- 

abstractions.    _  .  -    .  . 

ferred  to  by  an  abstract  term  as  a  sort  of  thing 

with  a  certain  independent  existence,  possessing  attributes  and 
playing  an  active  part  in  the  world  as  things  alone  can.  In 
this  way  '  life  ',  '  natural  laws  ',  '  motion  ',  '  force  ',  '  ideas  ', 
'justice',  'evil',  '  the  Zeitgeist ',  'Public  Opinion',  and  a 
host  of  other  abstractions  are  liable  "  to  play  the  part  of  sham- 
essences,  and  cheat  their  way  into  recognition  as  realities."  f 

*  The  word  '  thing  '  is  intended  here  and  is  usually  intended  elsewhere 
in  this  book  to  refer  to  whatever  possesses  substantial  reality.  It  there- 
fore includes  persons. 

\  Jas.  Martineau,  "  Study  of  Spinoza  ",  p.  12. 


HYPOSTATISING   ABSTRACTIONS.  67 

Nothing  exists  in  the  whole  universe  but  a  vast  number  of 
persons  and  things  acting  in  various  ways.  It  has  no  place 
for  abstractions.  To  say  that  a  person  has  an  idea  means 
that  he  thinks.  To  say  that  a  speaker  conveys  an  idea  to 
his  hearers  means  that  he  makes  them  know  what  he  thinks. 
To  say  that  a  smile  spread  through  the  company  means  that 
several  persons  smiled  at  once,  or  that  some  smiled  and 
then  others  smiled  because  they  saw  them  do  it.  To  say 
that  energy  is  stored  up  means  that  a  thing  is  not  acting, 
but  is  in  a  condition  to  act,  upon  occasion.  To  say  that 
motion  is  transmitted  means  that  one  thing  stops  moving  and 
another  begins.  Imagine  a  smile  spreading  through  a  com- 
pany like  water  through  a  sponge,  or  energy  stored  up 
like  grain  in  the  inner  recesses  of  a  thing,  or  motion  being 
carried  from  its  resting-place  in  one  thing  to  a  quiet  nook  in 
another  !  Public  opinion  is  only  what  is  similar  in  every- 
body's way  of  thinking  about  a  question.  A  law  is  nothing 
but  a  statement  of  how  people  must  act  if  they  wish  not 
to  be  punished  by  the  law-maker,  or  a  statement  of  how 
things  as  a  matter  of  fact  do  act  under  certain  circum- 
stances. It  is  not  some  shadowy  reality  existing  before  or 
apart  from  all  things  and  compelling  their  obedience  by  its 
own  strength.  A  law  is  never  imposed  on  things.  To  say 
that  two  chemicals  have  an  affinity  for  each  other  does  not  ex- 
plain why  they  combine  or  act  in  conjunction;  it  merely 
states  the  fact  that  they  do. — And  so  of  all  the  rest. 

The  habit  of  defining  abstract  nouns  rather  than  their  cor- 
responding verbs  and  adjectives  helps  to  entrap  us  in  this 
"snare  of  abstractions".  We  have  been  taught  to  say  that 
attraction  is  the  principle  or  power  in  virtue  of  which  one 
body  approaches  another,  or  that  beneficence  is  the  trait  of 
character  manifested  in  acts  of  general  kindness.  It  would 
be  better  to  say  that  one  thing  attracts  another  when  it  makes 
it  come  nearer,  and  that  a  person  is  beneficent  when  he  is 
kind  to  everybody.  "The  snare  of  abstractions  concealing 
itself  chiefly  in  common  nouns,  we  shall  best  guard  against  it 


68        THE   USES   OF   SINGLE   WORDS   AND   PHRASES. 

by  admitting  to  our  definition  no  substantive  where  an  adjec- 
tive [or  verb]  ought  to  serve  as  well."  * 

It  is  often  said  that  the  tendency  to  take  abstractions  for 
things  is  particularly  characteristic  of  philosophers.  This  is 
probably  not  true.  And  yet  the  philosopher  must  take  spe- 
cial care  to  overcome  it;  for  the  nature  of  his  work  is  such 
that  a  very  few  blunders  of  this  kind  can  spoil  it.  Hence 
the  advice  contained  in  the  following  quotation  is  excellent, 
and  the  criticism  implied  in  the  last  sentence  is  not  altogether 
unjust:  "If  the  student  of  philosophy  would  always,  or  at 
least  in  cases  of  importance,  adopt  the  rule  of  throwing  the 
abstract  language  in  which  it  is  so  frequently  couched  into  a 
concrete  form,  he  would  find  it  a  powerful  aid  in  dealing  with 
the  obscurities  and  perplexities  of  metaphysical  speculation. 
He  would  then  see  clearly  the  character  of  the  immense  mass 
of  nothings  which  constitute  what  passes  for  philosophy."  * 

Philosophy,  however,  is  not  the  only  subject  that  suffers  by 
this  tendency  to  take  abstractions  for  things,  as  can  be  shown 
by  the  following  passages  from  Langlois  and  Seignobos'  beau- 
tiful "  Introduction  to  the  Study  of  History  ",  already  quoted. 

"The  facts  of  society  are  of  an  elusive  nature,  and  for  the 
purpose  of  seizing  and  expressing  them,  fixed  and  precise 
language  is  an  indispensable  instrument ;  no  historian  is  com- 
plete without  good  language.  It  will  be  well  to  make  the 
greatest  possible  use  of  concrete  and  descriptive  terms  :  their 
meaning  is  always  clear.  It  will  be  prudent  to  designate 
collective  groups  only  by  collective,  not  by  abstract  names 
(Royalty,  State,  Democracy,  Reformation,  Revolution),  and  to 
avoid  personifying  abstractions.  We  think  we  are  simply 
using  metaphors,  and  then  we  are  carried  away  by  the  force 
of  the  words.  Certainly  abstract  terms  have  something  very 

*  Martineau.  Inc.  fir.  p.  124.  Lotzc  somewhere  says  about  the  same 
thing.  See  also  the  introduction  to  Berkeley's  "Principles  of  Human 
Knowledge  ". 

f  Bailey's  "Letters  on  the  Mind",  vol.  II,  p.  159,  quoted  by  Bam. 
"Logic",  p.  53. 


IIYPOSTATISING   ABSTRACTIONS.  69 

seductive  about  them,  they  give  a  scientific  appearance  to  a 
proposition.  But  it  is  only  an  appearance,  behind  which 
scholasticism  is  apt  to  be  concealed;  the  word,  having  no 
concrete  meaning,  becomes  a  purely  verbal  notion  (like  the 
soporific  virtue  of  which  Moliere  speaks)."  (Pp.  266-7). 

"Specialists,  influenced  by  a  natural  metaphor,  and  struck 
by  the  regularity  of  these  successions,  have  regarded  the  evo- 
lution of  usages  (of  a  word,  a  rite,  a  dogma,  a  rule  of  law), 
as  if  it  were  an  organic  development  analogous  to  the  growth 
of  a  plant ;  we  hear  of  the  '  life  of  words  ',  of  the  '  death  of 
dogmas',  of  the  'growth  of  myths'.  Then,  in  forgetfulness 
of  the  fact  that  all  these  things  are  pure  abstractions,  it  has 
been  tacitly  assumed  that  there  is  a  force  inhering  in  the 
word,  the  rite,  the  rule,  which  produces  its  evolution.  .  .  . 
Just  as  usages  have  been  treated  as  if  they  were  existences 
possessing  a  separate  life  of  their  own,  so  the  succession  of 
individuals  composing  the  various  bodies  within  a  society 
(royalty,  church,  senate,  parliament)  has  been  personified  by 
the  attribution  to  it  of  a  will,  which  is  treated  as  an  active 
cause.  A  world  of  imaginary  beings  has  thus  been  created 
behind  the  historical  facts,  and  has  replaced  Providence  in 
the  explanation  of  them.  For  our  defence  against  this  de- 
ceptive mythology  a  single  rule  will  suffice  :  Never  seek  the 
causes  of  an  historical  fact  without  having  first  expressed  it 
concretely  in  terms  of  acting  and  thinking  individuals.  If 
abstractions  are  used,  every  metaphor  must  be  avoided  which 
would  make  them  play  the  part  of  living  beings."  (Pp. 
288-9.)* 

• 

*  Abstract  terms  are  often  demonstrative  rather  than  descriptive.  To 
be  sure,  they  point  out  qualities  and  relations  which  have  no  independent 
existence  and  which  are  usually  best  indicated  by  descriptive  terms;  but 
whether  the  qualities  or  relations  in  question  have  such  an  existence  or 
not,  they  can  be  the  objects  of  thought,  and  when  they  are,  the  words 
used  to  point  them  out  are  demonstrative.  Indeed  we  may  go  so  far  as 
to  use  a  demonstrative  term  to  indicate  a  quality,  actor  relation  and 
a  descriptive  term  to  indicate  the  real  thing  without  which  it  could  not 


70        THE   USES   OF   SINGLE   WORDS   AND   PHRASES. 

The  term  '  Abstract '  is  often  applied,  with  a  somewhat 
broader  meaning  than  that  given  in  the  definition,  to  words 

which  indicate  complex  relations  that  are  not  eas- 
Secondary  ,  .  .  „,,  .  , 

meaning  of      ily  perceived  by  the  senses.      ihus  we  might  say 

that  when  the  words  'free'  and  'equal*  are  used 
to  mean  '  not  tied  or  locked  up  '  and  '  of  the  same  size '  they 
are  concrete  ;  but  when  they  are  used  ('  in  the  second  inten- 
tion') to  mean  what  politicians  mean  when  they  say  that  all 
men  are  born  '  free  and  equal '  they  are  abstract.  The  first 
relations  can  be  easily  perceived  by  the  senses  and  easily 
defined  ;  the  second  can  not.  In  the  same  way  the  terms 
'universe',  'siderial  system',  &c.,  might  be  called  ab- 
stract.* 

General  terms  are  used  to  distinguish  objects  which  possess 
certain  characteristics  from  those  which  do  not.  They  are 

exist,  as  when  we  speak  of  '  Asiatic  duplicity  ',  '  the  Turkish  atrocities  ',  or 
'  the  Franco  German  war'. 

*  Abstract  and  Concrete  words  are  often  distinguished  by  their  form  ; 
but  '•  unfortunately  "  the  two  forms  "  are  frequently  confused,  and  it  is  by 
no  means  always  easy  to  distinguish  the  meanings.  Thus  '  relation  ' 
properly  is  the  abstract  name  for  the  position  of  two  people  or  things  to 
each  other,  and  those  people  are  properly  called  'relatives'  (Latin  rela- 
tions, one  who  is  related).  But  we  constantly  speak  now  of  'relations', 
meaning  the  persons  themselves  ;  and  when  we  want  to  indicate  the  ab- 
stract relation  the}'  have  to  each  other  we  have  to  invent  a  new  abstract 
term,  '  relationship  '.  '  Nation '  has  long  been  a  concrete  term,  though 
from  its  form  it  was  probably  abstract  at  first  ;  but  so  far  does  the  abuse 
of  language  now  go,  especially  in  newspaper  writing,  that  we  hear  of  a 
'nationality'  meaning  a  nation,  although  of  course  if  'nation'  is  the 
concrete.  '  nationality '  ought  to  l>e  the  abstract,  meaning  the  quality  of 
being  a  nation.  Similarly  '  action',  'intention',  'extension',  'conception', 
and  a  multitude  of  other  properly  abstract  names,  are  used  confusedly 
for  the  corresponding  concrete,  namely  'act',  'intent',  'extent',  'con- 
cept ',  etc.  '  Production  '  is  properly  the  condition  or  state  of  a  person 
who  is  producing  or  drawing  something  forth  ;  but  it  has  now  become 
confused  with  that  which  is  produced,  so  that  we  constantly  talk  of  the 
'  productions '  of  a  country,  meaning  the  'products'.  .  .  .  Much  injury 
is  done  to  language  by  this  abuse  "  (Jevons,  ''Elementary  Lessons  in 
Logic  ",  p.  21). 


POSITIVE   AND   NEGATIVE.  71 

usually  applied  to  the  objects  which  possess  the  characteristic 

in  question,  but  they  can  be  so  altered  as  to  ap- 

Positive 

ply — or  wholly  different  terms  can  be  invented   and 

negative. 

which  apply — only  to  the  objects  which  do  not 

possess  the  characteristic  in  question.  General  terms  of  the 
first  sort  are  called  Positive,  those  of  the  second  sort  Negative. 
The  words  '  Jesv  ',  'Greek',  'citizen',  'clergyman',  'edu- 
cated', 'Aryan',  'white',  are  positive  terms.  Their  cor- 
responding negatives  are  'Gentile',  'barbarian'  (in  the 
earlier  sense  of  the  word),  'alien ',  '  layman  ',  '  uneducated  ', 
'non-Aryan',  'not  white'.  Where  negative  terms  do  not 
exist  they  can  always  be  made  by  attaching  some  such  prefix 
as  'in-',  'un-',  'non-',  or  'not-',  or  some  such  suffix  as 
'-less  '  to  a  positive  term  ;  but  we  must  not  take  it  for  granted 
that  terms  which  have  these  affixes  always  correspond  in 
meaning  in  this  way  with  those  that  have  not.  It  is  said  that 
a  college  chaplain  once  became  sleepy  during  a  service  and 
implored  the  irreligious  to  become  religious  ;  the  immoral, 
moral  ;  the  intemperate,  temperate  ;  the  inebriate,  ebriate  ; 
and  the  indifferent,  different ! 

Sometimes  terms  which  are  negative  in  form  have  a  positive 
meaning,  and  vice  versa.  Thus  the  terms  'uncomfortable', 
'unhappiness ',  'uneasiness',  are  all  used  to  indicate  that 
disagreeable  feelings  are  present,  and,  on  the  other  hand, 
the  terms  'free',  'sober',  and  'healthy'  are  used  to  indi- 
cate that  certain  undesirable  conditions  are  absent.  The 
terms  '  moral '  and  '  good  '  are  probably  more  often  used  in 
a  negative  sense  than  in  a  positive. 

Though  negative  terms  are  used  to  indicate  the  absence  of 
certain  characteristics,  they  are  not  properly  applicable  to 
everything  which  does  not  possess  these  characteristics.  A 
mutton-chop  is  neither  a  Jew  nor  moral  nor  able  to  see,  but 
neither  is  it  a  Gentile  nor  immoral  nor  blind.  A  man,  on 
the  other  hand,  must  be  one  or  the  other.  Negative  terms 
are  thus  only  applicable  to  things  that  are  capable  of  posses- 
sing, or  might  reasonably  be  supposed  to  possess,  the  char- 


72        THE   USES   OE  SINGLE   WORDS   AND   PHRASES. 

acteristics  whose  absence  the  negative  term  denotes.  They 
are  used  with  reference  to  what  De  Morgan  has  called  a 
limited  universe  of  discourse.  Within  that  universe,  but  not 
beyond  it,  everything  can  be  described  either  by  a  positive 
term  or  by  the  corresponding  negative.  In  the  example  just 
given  the  universe  of  discourse  was  human  beings.  If  we  say 
that  everything  must  be  either  light  or  heavy,  here  or  there, 
we  have  in  mind  the  universe  of  tangible  objects  existing  in 
space.  The  statement  would  not  be  true  of  a  soul  or  a 
feeling  of  remorse.  When  Euclid  says  that  things  which  are 
equal  to  the  same  thing  are  equal  to  one  another,  his  universe 
of  discourse  is  the  sixe  of  lines  or  figures.  If  A  is  equal  to  B 
in  social  position  and  B  is  equal  to  C  in  intelligence,  it  does 
not  follow  that  there  is  any  respect  in  which  A  is  equal  to  C. 

There  are  a  vast  number  of  words  whose  meaning  is 
ambiguous  until  one  knows  the  universe  of  discourse  to  which 
they  refer.  The  term  'irregular',  for  example,  may  have 
reference  to  the  distribution  of  lines  in  space,  or  the  succes- 
sion of  events  in  time,  or  a  person's  moral  relations. 

Which  of  two  mutually  exclusive  terms,  one  or  other  cf 
which  is  applicable  to  every  individual  in  a  given  universe  cf 
discourse,  is  to  be  regarded  as  negative  is  often  a  matter  of 
indifference,  for  within  a  given  universe  the  absence  of  one 
characteristic  involves  the  presence  of  another  belonging  to 
the  same  general  class.  A  substance  which  is  immaterial 
must  be  spiritual,  a  thing  which  we  take  the  trouble  to 
describe  as  not  white  is  usually  a  kind  of  thing  that  must 
have  some  color  or  other.  There  is  as  much  fulness  of 
determination — there  are  as  many  attributes — in  one  case  as 
in  the  other. 

Though  '  immaterial  '  and  '  not  white  '  are  both  terms 
which  imply  the  presence  of  some  corresponding  attribute, 
there  is  this  difference  between  them  :  in  the  one  case  we 
know  immediately  what  the  attribute  is — the  thing  must  be 
spiritual  ;  in  the  other  \ve  do  not,  for  the  thing  may  have  any 
one  of  many  colors.  Thus  when  there  are  only  two  alterna- 


RELATIVE  AND   ABSOLUTE:    FIRST   SENSE.  73 

tives,  a  term  which  indicates  the  absence  of  one  of  them  lias 
a  definite  positive  significance;  when  there  are  many  the  pos- 
itive significance  is  indefinite. 

A  positive  term  and  its  negative  are  called  with  reference 
to  each  other  negative,  contradictory,  or  more  properly,  con- 
irapositive  terms. 

Some  terms  (such  as  '  giant ' ,  '  dwarf ' ;  '  immense  ',  '  tiny  ' ; 
'courageous',  'cowardly';  'noble',  'ignoble')  are  used 
to  name  contrasting  and  mutually  exclusive  relations;  but 
there  are  objects  in  the  universe  of  discourse  to  which  neither 
term  in  such  a  pair  is  applicable.  There  are  many  men 
who  are  neither  giants  nor  dwarfs,  many  acts  that  are  neither 
noble  nor  ignoble.  In  such  cases  the  terms  are  not  Con- 
tradictories, but  contraries  or  opposites. 

Whether  such  terms  as  '  thin  '  and  '  thick  ',  '  large  '  and  ] 
'small '  are  contrary  or  contradictory  depends  upon  the  circum- 
stances in  which  they  are  used.  The  frequent  controversies 
to  which  they  give  rise  in  this  respect  are  due  to  the  fact  that 
they  are  never  terms  of  precision  in  any  respect.  When  we  wish 
to  be  accurate  we  give  measurements.  Neither  speaker  nor 
hearer  usually  stops  to  ask  what  size  a  thing  must  be  in  order 
to  be  large  or  small;  they  therefore  do  not  ask  whether  there 
can  be  anything  of  the  kind  discussed  which  is  neither  large 
nor  small.  To  raise  the  question  is  to  attempt  to  render 
definite  the  meaning  of  terms  whose  value  lies  in  their  essen- 
tial vagueness.  Hence  the  old  catch  called  Sorites  :  '  How 
many  things  does  it  take  to  make  a  heap  ?  ' 

The  last  distinction  between  terms  which  we  shall  have  to 
consider  is  between  Relative  and  Absolute.  Unfortunately 

there   are   two  distinct   senses   in   which   a  term 

......  ,        .       -  r  Relative  and 

can  be  said  to  be  relative.      In   the  first  sense  oi   absolute : 
,  ,  .          ,  i     i    -r^    i     •  i  /        first  sense, 

the  word   a  term    is   called   Relative   when    (as 

with   'master',    'combatant',    'lover')    it   is  applied  to   a 

person  or  thing  to  mark  a  certain  active   relation   to  some 

other  person  or  thing  *, — a  relation  which  might  have  been 

*  These  relative  terms  are  usually  nouns  or  words  used  as  such,  t.g., 


74        THE   USES   OF   SINGLE  WORDS   AND   PHRASES. 

expressed  by  a  transitive  verb  or  a  phrase  involving  one. 
Such  names  are  usually  found  in  pairs  called  correlatives,  one 
for  each  party  to  the  relation,  e.g. ,  'master',  'servant'; 
'landlord',  'tenant';  'debtor',  'creditor':  'victor', 
'  vanquished  '  ;  '  lover  ',  '  beloved  '. 

We  might  avoid  the  use  of  such  terms  by  saying  that  one 
person  works  for  another,  or  has  rented  his  house,  or  has 
borrowed  money  from  him  and  not  yet  paid  it  back,  and  so 
forth.  In  a  world  in  which  nothing  affected  anything  else 
this  first  kind  of  relative  terms  would  have  no  place.  They 
express  a  relation  existing  only  between  two  active  beings. 
Relative  terms  of  the  second  kind,  on  the  other  hand — of 
which  we  are  about  to  speak — express  no  action  of  one  thing 
upon  another,  but  merely  the  fact  that  some  one  has  com- 
pared them  in  a  given  respect. 

In  the  second  sense  of  the  word  terms  are  called  '  Relative  ' 
when,  like  such  words  as  'larger',  they  indicate  the  result  of 
Second  a  comParison  with  some  standard  which  the  term 

sense.  itself  does  not  indicate.  The  most  obvious  ex- 

amples of  such  terms  are  adjectives  of  the  comparative  de- 
gree, for  with  them  it  is  necessary  to  name  the  standard  in 
some  added  words  in  order  to  give  the  term  any  meaning, 
e.g. ,  '  A  robin  is  larger  than  a  sparrow  '.  With  superlatives  we 
recognize  that  a  standard  is  involved  though  we  do  not  always 
mention  it,  e.g. ,  '  I  saw  the  loveliest  picture  '.  Such  expressions 
as  '  rather  beautiful  ',  'very  beautiful  ',  'extremely  beautiful  ', 
'most  beautiful'  (not  distinguished  in  Latin  from  ordinary 
comparatives  and  superlatives)  also  involve  some  reference  to 
a  standard.  By  a  '  rather  beautiful '  thing  we  mean  one  that 
is  perhaps  somewhat  more  beautiful  than  the  average  of  its 
kind  ;  by  an  '  excellent '  piece  of  work,  one  that  is  exception- 
ally good. 

my  heloTed.  They  are  perhaps  occasionally  adjectives  :  e.g. ,  parental, 
though  I  am  not  sure  whether  this  should  really  be  called  a  relative  term 
or  not.  They  arc  almost  always  applied  to  persons,  though  not  always  : 
'•£-,  reagent. 


SECOND   SENSE.  75 

It  is  less  obvious,  but  no  less  true,  that  an  immense  number 
of  terms  '  positive  '  in  form  are  really  used  in  a  comparative 
or  relative  sense.  A  large  thing  is  larger  than  a  small  thing, 
a  clean  thing  cleaner  than  a  dirty  thing,  an  intelligent  creature 
more  intelligent  than  a  dull  one ;  but  a  large  rat  is  not  neces- 
sarily larger  than  a  small  elephant,  a  clean  stable  cleaner  than 
a  dirty  table-cloth,  or  an  intelligent  horse  more  intelligent 
than  a  dull  man.  In  each  of  these  cases  the  name  of  the 
thing  to  which  the  adjective  is  applied  indicates  the  standard 
of  comparison.  A  large  rat  is  one  larger  than  most  other 
rats ;  an  intelligent  horse,  one  more  intelligent  than  most 
other  horses  ;  a  clean  stable,  one  cleaner  than  most  others, 
or  as  clean  as  one  could  reasonably  hope  to  keep  a  stable.  A 
rat  is  an  animal,  but  \ve  cannot  say  that  a  large  rat  is  a  large 
animal,  because  the  standard  of  largeness  changes  as  we  pass 
from  the  consideration  of  rats  to  that  of  animals  in  general. 
What  we  have  a  right  to  say  is  that  a  large  rat  is  an  animal 
larger  than  most  rats.  In  this  way  we  retain  the  meaning  of 
the  word  '  large  '  with  which  we  started. 

Amongst  other  kinds  of  inference  Jevons  mentions  Imme~ 
diate  Inference  by  added  Determinants,  which  "consists  in 
joining  some  adjective  or  similar  qualification 
both  to  the  subject  and  predicate  of  a  proposition." 
Hyslop  says  of  it  that  terms  expressing  quantity,  such  as 
'large',  'long',  'small',  'short',  must  be  used  carefully; 
but  that  terms  expressing  quality  "can  be  used  with  perfect 
freedom,  provided  they  are  not  used  equivocally".*  If 
more  examples  are  needed  to  show  that  this  is  not  the  case 
there  are  plenty  to  be  had.  An  Australian  Bushman  is  a 
man,  but  an  intelligent  Bushman  is  not  an  intelligent  man, 
a  respectable  saloon  is  hardly  a  respectable  place,  an  ener- 
getic snail  an  energetic  animal,  nor  a  fast  mule-car  a  fast 
means  of  transportation. 

This   "inference  by  added  determinants"   gives  a  good 

*  Elements  of  Logic,  p.  168  (Scribners,  1894.      Third  Edition). 


76        THE   USES   OF   SINGLE   WORDS   AND   PHRASES. 

illustration  of  the  trouble  we  get  into  when  we  substitute  rules 
of  verbal  manipulation  for  thought  about  the  things  that  the 
words  are  intended  to  denote. 

The  following  passage  from  Schopenhauer  shows  how  even 
a  first-class  author  is  likely  to  deceive  himself  and  his  readers 
when  he  makes  too  much  use  of  relative  terms.  The  passage 
seems  to  be  full  of  meaning,  but  it  turns  out  on  analysis  to  be 
absolutely  empty. 

"This  human  world  is  the  kingdom  of  chance  and  error. 
...  [i]  Everything  better  only  struggles  through  with 
difficulty;  what  is  noble  and  wise  seldom  attains  to  expres- 
sion, becomes  effective  and  claims  attention,  but  [2]  the 
absurd  and  perverse  in  the  sphere  of  thought,  the  dull  and 
tasteless  in  the  sphere  of  art,  the  wicked  and  deceitful  in  the 
sphere  of  action,  really  assert  a  supremacy,  only  disturbed 
by  short  interruptions.  On  the  other  hand  [3]  everything 
that  is  excellent  is  always  a  mere  exception,  one  case  in 
millions,  and  therefore  if  it  presents  itself  in  a  lasting  work, 
this,  when  it  has  outlived  the  enmity  of  its  contemporaries, 
exists  in  isolation,  is  preserved  like  a  meteoric  stone,  sprung 
from  an  order  of  things  different  from  that  which  prevails 
here."  * 

These  words  mean  something  like  this  :  '  I  am  dissatisfied 
with  the  world  because  [i]  the  exceptionally  good  is  excep- 
tional, [2]  what  is  no  better  [and  no  worse]  than  the  com- 
mon is  common,  and  [3]  anything  good  that  is  exceptional 
enough  for  me  to  call  it  excellent  is  very  exceptional  indeed.' 
If  the  value  of  everything  in  the  world  were  increased  a 
thousandfold  a  new  philosopher  who  happened  to  feel  dis- 
satisfied could  use  Schopenhauer's  very  words,  for  '  good  ' 
and  '  bad  '  would  be  interpreted  then  as  they  are  now  with 
reference  to  the  average. 

*  "The  World  as  Will  and  Idea",  Vol.  I,  p.  417  (Kegan  Paul,  Trench, 
TrUbner  &  Co.,  1891). 


CHAPTER  VI 

THE   RELATIONS   EXPRESSED   IN  PROPOSITIONS 

THE  meaning  of  words  and  statements  has  been  discussed 
enough  in  the  foregoing  chapters  to  guard  against  various 
kinds  of  rather  gross  blunders.  Our  next  task  is  to  inquire 
what  fundamental  relations  of  things  statements  of  various 
kinds  imply.  This  is  the  work  of  the  present  chapter.  In 
the  next  we  shall  carry  the  same  subject  further  by  inquiring 
what  any  proposition  implies  about  the  existence  of  the 
things  it  mentions.  After  these  more  general  discussions 
we  shall  come  back  and  consider  propositions  from  a  more 
formal  standpoint,  taking  up  the  difference  between  various 
forms  of  statement,  the  significance  of  each,  and  the  way  in 
which  a  statement  in  one  form  of  words  may  imply  the  truth 
or  falsity  of  a  statement  in  some  other  form  of  words. 

'  This  is  John  ' ;  '  John  is  happy  ' ;  '  John  is  riding  a  horse  '. 
It  is  perfectly  evident  that  in  these  propositions  the  rela- 
tions expressed  by  the  verb  ( is '  are  wholly  different  and 

incomparable.     In  the  first  case  it  helps  to  identify 

i  i    •    i    i  11  i  •        Five 

a  person  ;  in  the  second,  it  helps  to  tell  something   fundamental 

,.  ,       .       ,        ..,.,,  relations, 

about  his  state  of  mind  ;   in  the  third,  it  helps  to 

tell  his  relation  to  something  else  How  many  absolutely 
different  kinds  of  relation  we  can  think  of  and  express  in 
propositions  it  is  hard  to  say.  The  question  is  one  whose  full 
discussion  belongs  to  metaphysics  rather  than  to  logic  ;  and 
it  is  one  about  which  metaphysicians  have  not  agreed. 
Nevertheless,  something  should  be  said  about  it  here  ;  for  the 

77 


7  8      THE   RELATIONS   EXPRESSED   IN  PROPOSITIONS. 

very  first  rule  of  logic  is  to  understand  the  meaning  of  the 
words  we  use. 

In  thinking  about  the  question  it  is  well  to  remember  that 
in  reality  nothing  exists  but  things  (including  persons)  with 
their  various  attributes  and  acts.  The  following  list  is  per- 
haps as  good  as  any. 

1.  We  are  able,  first  of  all,  to  distinguish  between  various 
individual  things  and  to  recognize  the  fact  that  through  all 
the  changes   they   undergo  each   one   of  them  remains   the 
same  :   the  Paul  who  preached  Christ  was  identical  with  the 
Saul   who   was    present  at  Stephen's  death,  in   spite  of  his 
change  of  heart  and  name  in  the  meantime  ;    the  rock   on 
Emerson's  grave  to-day  is  the  very  same  rock  that  was  there 
yesterday  and  that  was  carried  there  years  ago.     Precisely 
what  it  is  that  makes  a  thing  to  be  the  same  throughout  all 
its  changes  of  state  and  circumstances, — whether  the  ship  of 
Argos,    repaired   so  often   that  at   last   none   of  the  original 
material  remained,  was  really  the  same  ship  or  not, — this  is 
a  detail  of  metaphysics  which  we  cannot  discuss  here.      But 
in  a  general  way  every  one  knows  what  it  is  to  recognize  an 
old  friend,  or  to  say  that  he  himself  is  the  very  person  who 
performed  such  and  such  an  act,    or  that  the  book  in  his 
hand  is  not  the  one  he  bought  yesterday,  though  the  two  look 
precisely  alike. 

The  first  kind  of  proposition,  then,  is  that  which  asserts  or 
denies  this  unity  or  individual  identity  of  a  thing  that  then 
was  there  or  did  that,  with  one  that  afterwards  was  here  or 
did  this. 

It  is  evident  that  any  proposition  of  this  kind  must  in- 
volve two  demonstrative  terms  connected  by  the  verb  to  be, 
e.g.,  This — is — the  man  who  was  here  yesterday. 

2.  The   second  kind   of  relation   affirmed   or  denied  by 
propositions   is   that   which    exists   between  a  thing   and  its 
qualities,  states,  or  activities   (whether  we  suppose  it  to  be 
conscious  of  these  or  not);    in  short,  it  is  a  relation  of  subject 
and  attribute,  eg.:'  Bulldogs  are  courageous  '  ;    '  this  iron  is 


FIVE   FUNDAMENTAL   RELATIONS.  79 

not  cold  ';  '  he  laughed  ';  '  he  is  asleep'.  The  subject  of  such 
propositions  is  always  a  demonstrative  term  ;  the  predicate  is 
always  descriptive,  but  its  meaning  may  be  expressed  either 
by  the  verb  to  le  or  its  equivalent  (i.e.,  to  seem,  to  appear,  or 
some  other  similar  verb)  followed  by  an  adjective  or  its 
equivalent  {i.e.,  some  descriptive  noun  or  phrase),  or  merely 
by  an  intransitive  verb  (with  or  without  a  completing  or 
modifying  adverb),  e.g. :  '  He  is  insane';  'he  is  a  lunatic'; 
'  he  raves  ';  '  he  acts  insanely  '. 

3.  The  third  kind  of  relation  affirmed  or  denied  by  propo- 
sitions is  the  action  of  one  thing  upon  another,  or  the  mutual 
relations  of  two  things  as  active  beings.  Propositions  ex- 
pressing such  relations  involve  two  demonstrative  terms  and 
a  transitive  verb  or  its  equivalent,  e.g. :  'John  strikes  his 
horse';  '  A.  and  B.  are  quarreling';  '  C.  is  D.'s  landlord', 
i.e.,  rents  a  house  to  him;  '  E.  walks  on  the  grass',  i.e., 
treads  the  grass.  These  relations  may  be  called  causal  or 
dynamic. 

Whether  a  proposition  belongs  to  this  third  class  or  to  the 
second  is  often  a  mere  question  of  interest.  A  man  cannot 
walk  without  treading  upon  something,  but  we  are  not  usu- 
ally interested  in  the  effect  upon  the  object  beneath  his  feet, 
and  so  we  regard  the  statement  that  he  walks  as  merely 
descriptive.  When  we  are  interested  enough  to  tell  what 
he  walks  upon  the  dynamic  relation  becomes  prominent. 
Further,  as  Sigwart  says  in  his  "Logic":*  "  When  a  man 
walks  he  moves  his  legs;  that  which  from  one  point  of  view- 
is  mere  action  appears  from  another  as  an  effect  upon  his 
limbs,  which  are  relatively  independent  things."  Here, 
again,  the  classification  of  the  proposition  depends  upon  the 
interest  which  one  can  reasonably  be  supposed  to  take  in 
some  particular  aspect  of  the  whole  fact  stated. 

Sometimes,  but  not  usually,  it  is  proper  to  regard  a  state- 
ment of  a  thing's  color,  taste,  smell,  or  other  perceptible 

*  Vol.  I,  p.  37  (Macmillan) 


So      THE   RELATIONS   EXPRESSED   IX   PROPOSITIONS. 

quality  as  dynamic  rather  than  merely  descriptive;  for  to 
have  a  certain  color  is  to  reflect  light  in  a  certain  way,  and 
to  have  a  certain  smell  is  to  act  chemically  in  a  certain  way 
upon  an  olfactory  organ.  But  when  the  ultimate  nature  of 
things  is  not  under  discussion  it  is  more  convenient  to  ignore 
these  facts  and  regard  such  statements  as  merely  descriptive. 
4.  Propositions  of  the  fourth  kind  affirm  or  deny  the  exist- 
ence of  various  non-dynamic  or  non-causal  relations  between 
two  or  more  different  things  or  other  objects  of  thought. 
They  express  our  comparisons  between  them  rather  than  the 
action  of  one  upon  another.  We  may  say,  for  example,  that 
several  objects  are  similar  or  dissimilar;  that  things  or  events 
coexist  or  succeed  each  other  in  time  ;  that  they  bear  to  each 
other  various  relations  in  space  ;  that  one  thing  is  more  or  less 
beautiful,  one  musical  note  'higher'  or  'lower',  or  one  man 
morally  better  or  ivorse  than  another,  without  supposing  the 
objects  whose  relations  we  discuss  to  affect  each  other  in  any 
way  whatever.  The  number  of  relations  of  this  kind  which 
anything  bears  to  anything  else  is  limited  only  by  the  ability 
of  beings  that  know  them  both  to  compare  them  together  in 
various  respects  ;  and  whether  many  or  few  such  relations  be 
discovered  or  exist  has  not  the  slightest  effect  upon  the 
things  compared  or  their  activities.  Causal  relations,  on  the 
other  hand,  engross  more  or  less  of  a  thing's  energy,  and 
may  thus  interfere  with  each  other.  Anything,  A,  might 
resemble  B,  coexist  with  C,  be  heavier  than  D,  lighter  than 
E  and  beside  F,  all  at  once;  but  if  A  were  a  man  he  could 
not  at  any  one  time  fight  with  B,  dance  with  C,  and  discuss 
philosophy  with  D.  Causal  relations  exist  direct! v  for  the 
things  related,  and  seem  to  penetrate  into  and  affect  their 
inmost  being;  non-dynamic  relations  concern  nothing  and 
nobody  but  the  being  that  discovers  them. 

The  most  important  of  the  non-dynamic  relations  are 
those  of  Space  and  Time,  without  which  the  mathematical 
sciences  would  be  impossible.  They  are  ^o  important  that 
many  eminent  writers  give  them  a  separate  place  in  their 


FIVE   FUNDAMENTAL   RELATIONS.  81 

lists  of  relations.  Indeed  relations  of  time  and  space  are 
often  supposed  to  comprehend  causal  relations.  The  ques- 
tion is  one  of  metaphysics  which  cannot  be  discussed  here.* 

When  we  speak  of  the  color  or  of  any  other  attribute  of  an 
object  as  identical  with  that  which  exists  elsewhere,  the  rela- 
tion asserted  is  really  a  relation  of  resemblance  rather  than  of 
individual  identity.  We  merely  mean  that  the  similarity  is 
complete.  We  must  not  be  deceived  by  a  merely  verbal 
resemblance  between  two  propositions.  If  I  say  that  your 
clothes  are  the  same  as  mine  the  relation  in  question  is  one  of 
resemblance  ;  if  I  say  that  they  are  the  same  that  you  wore  a 
year  ago  the  relation  is  one  of  identity.  If  I  say  the  house  has 
the  same  color  it  had  ten  years  ago  the  relation  indicated  by 
the  word  'same'  is  one  of  similarity  ;  if  I  say  it  has  the  same 
paint  the  relation  is  probably  intended  to  be  one  of  individual 
identity.  The  distinction  here  pointed  out  between  the  same 
thing  and  the  same  kind  of  thing  is  very  important,  though 
sometimes  lost  sight  of,  in  metaphysical  discussions.  In  which 
sense,  for  example,  do  we  see  the  same  rainbow  when  the  sun 
comes  out  again,  and  have  the  same  idea  or  make  '  the  very 
same '  remark  as  somebody  else  ? 

5.  So  far  we  have  discussed  the  various  relations  which  exist 
between  the  things  we  know  or  think  about,  but  we  have  said 
nothing  about  our  knowledge  of  these  relations.  It  is  one 
thing  for  the  frog  that  exists  to-day  to  be  identical  with  the 
tadpole  that  existed  six  months  ago,  and  quite  another  thing 
for  you  or  me  to  recognize  that  it  is  identical;  one  thing  for 

*  It  may  occur  to  the  reader  that  the  non-dynamic  relations  between 
several  objects  can  be  affirmed  or  denied  only  because  the  things  com- 
pared act  upon  the  person  making  the  comparison,  e.g.,  that  we  say  one 
thing  is  prettier  than  another  because  it  acts  upon  our  senses  in  such  a 
way  as  to  give  us  more  aesthetic  enjoyment.  This  is  often  the  case,  but 
we  must  not  infer  from  it  that  the  non-dynamic  relations  can  be  resolved 
into  dynamic,  for  even  if  we  suppose  that  to  be  pretty  means  merely  to 
please  the  beholder,  in  the  example  given  there  is  still  a  comparison  ex- 
pressed between  the  amount  of  enjoyment  present  in  the  two  cases.  'We 
cannot  therefore  get  rid  of  the  element  of  mere  comparison. 


32      THE   RELATIONS   EXPRESSED   IN   PROPOSITIONS. 

a  man  to  be  angry,  and  quite  another  thing  for  us  or  even  for 
the  man  himself  to  know  that  he  is  angry  ;  one  thing  for  A  to 
be  larger  than  B,  or  to  be  near  B,  or  to  influence  B,  and  quite 
another  thing  for  us  to  know  or  think  about  these  relations. 

We  have  thus  a  new  kind  of  relation  to  deal  with,  namely, 
thaH  between  a  person  thinking  and  the  thing  he  thinks  about 
— between  thought  and  its  object.  This  relation  can  be  called 
noetic. 

This  noetic  relation,  or  relation  between  thought  and  its 
object,  can  be  affirmed  or  denied  like  any  other:  e.g. ,  I  was 
thinking  of  you  ;  I  love  you  or  fear  you  ;  I  do  not  desire  a 
certain  end;  he  knew,  or  was  mistaken,  or  was  doubtful  about 
a  certain  matter;  your  ieeis  about  it  are  consistent,  or  con- 
tradictory, or  absurd ;  he  is  right  about  it  ;  he  thought  he 
knew ;  I  mean  you.  In  all  these  cases  something  is  said 
about  some  aspect  of  the  relation  between  a  thinker  or  his 
thought  and  the  object  thought  about. 

In  the  history  of  philosophy  much  has  been  made  of  the 
distinction  between  real  and  verbal  propositions  (otherwise 
called  Synthetic  and  Analytic,  Ampliative  and  Explicative, 
Accidental  and  Essential).  A  Real  proposition  tells  something 
about  an  object,  eg.  :  'A  thrush  is  in  the  tree',  '  Tully  is 
dead  '.  A  Verbal  proposition  tells  the  meaning  or  part  of  the 
meaning  of  a  word,  e.g. :  '  A  thrush  is  a  kind  of  bird  ',  '  Tully 
is  Cicero  '.*  Every  definition  is  thus  a  verbal  proposition. 
Euclid's  definitions  are  supposed  to  be  merely  verbal — telling 
nothing  more  than  the  meaning  of  words  ;  his  axioms  and 
postulates  to  be  real  — telling  something  more  than  the  names 
of  various  figures  strictly  imply,  though  perhaps  not  more 
than  everybody  knows.  Real  propositions  may  belong  to  any 
one  of  our  five  classes.  Verbal  propositions  are  always 
noetic  ;  for  to  tell  the  meaning  of  a  word  is  to  tell  of  what  I 

*  Contrast  with  these  propositions  such  a  one  as  this:  'That  man's 
name  is  Washington  Jefferson  Madison  Stokes'.  Here  the  name  is  re- 
garded as  a  kind  of  appendage,  and  the  proposition  is  as  descriptive  as 
if  it  had  been  said  that  the  man  had  thirteen  fingers. 


FIVE   FUNDAMENTAL   RELATIONS.  83 

am  thinking  and  of  what  I  wish  my  hearer  to  think  when  I 
use  it.* 

It  is  probable  that  we  can  never  speak  or  think  of  a  relation 
not  included  in  this  list :  Individual  Identity,  Subject  and 
Attribute,  Causal  relations  between  several  things,  Non-dy- 
namic, or  Non-causal,  relations  between  several  things,  and 
relations  between  thought  and  its  object  or  Noetic  relations. 
These  then  are  the  so-called  categories  ;  but  it  must  be  remem- 
bered that  the  fourth  class  includes  a  great  many  different 
relations  which  agree  in  only  one  respect,  namely,  that  they 
involve  at  least  two  objects  without  involving  any  action  of 
the  one  upon  the  other,  f 

*  The  terms  Real  and  Verbal  seem  to  me  preferable  to  Kant's  Syn- 
thetic and  Analytic,  partly  because  as  Mansel  says,  "  propositions  in  which 
the  predicate  is  a  single  term  synonymous  with  the  subject "  cannot  pos- 
sibly involve  any  analysis  or  splitting  up  of  the  meaning  of  the  subject; 
e.g.,  Tully  is  Cicero  (see  Keynes,  "Logic  ",  p.  43,  3d  ed.)  ;  but  mainly 
because  the  term  Analytic  implies  that  both  subject  and  predicate  of 
verbal  propositions  are  always  used  in  a  connotative  or  descriptive  sense 
and  that  the  function  of  such  propositions  is  to  analyze  ideas  rather  than 
to  identify  things  spoken  of.  In  a  word,  Kant's  terminology  does  not 
suggest  any  clear  distinction  between  thought  and  its  object. 

•(•Aristotle's  list  of  categories  is  as  follows:  Substance,  Quantity,  Qual- 
ity, Relation,  Action,  Passion,  Place.  Time,  Posture,  Habit. 

Hume  gives  Resemblance,  Identity,  Space  and  Time,  Quantity  or 
Number,  Degree  of  Quality,  Contrariety,  Cause  and  Effect. 

Kant  gives  Space  and  Time  and  four  sets  of  'pure  conceptions  ',  viz., 
Quantity,  including  Unity,  Plurality,  Totality;  Quality,  including  Real- 
ity, Negation,  Limitation  ;  Relation,  including  Substance  and  Accident, 
Cause  and  Effect,  Reciprocity  between  the  active  and  the  passive; 
Modality,  including  Possibility  and  Impossibility,  Existence  and  Non- 
existence,  Necessity  and  Contingency. 

Mill  gives  Sequence,  Coexistence,  Simple  Existence,  Causation,  Re- 
semblance. 

For  an  explanation  of  Aristotle's  list  see  Minto's  "  Logic  ",  Chap.  III. 
Hume's  categories,  called  by  him  "philosophical  relations  ",  are  enumer- 
ated and  explained  in  the  "Treatise  of  Human  Nature",  Bk.  I,  Pt.  I, 
Sec.  V.  But  his  discussion  of  Space  and  Time  and  Causation  runs 
through  the  first  three  '  Parts '.  Kant's  categories,  which  he  makes  to 
correspond  with  the  formal  differences  between  propositions  as  set  forth 


84      THE    RELATIONS   EXPRESSED   IX   PROPOSITIONS. 

Since  abstract  propositions  can  always  be  reduced  to  con- 
crete, it  is  evident  that  no  new  class  of  relations  need  be  made 
on  their  account. 

Though  these  relations  are  probably  all  we  can  think  of, 
they  are  often  so  combined  as  to  give  the  appearance  of  some- 
thing quite  different  from  any  of  them.     The  rela- 
Certain 
combined         tion  of  means  and  end,  for  example,  is  made  up  of 

a  desire  for  something  (a  noetic  relation)  and  an 
attempt  to  get  it  (any  one  of  the  five  relations,  depending 
upon  the  kind  of  object  desired)  by  acting  on  certain  things 
(causal)  in  such  a  way  that  they  in  turn  will  do  something  that 
will  lead  (causal)  to  the  attainment  of  the  desire.  Change 
again,  is  an  alteration  (time)  in  the  states  (subject  and  attri- 
bute) or  outer  relations  (causal  or  non-dynamic)  of  a  thing 
which  remains  self-identical  throughout  them  all  (individual 
identity).  This  case  of  Change  shows  how  inextricably  dif- 
ferent categories  are  sometimes  interwoven. 

The  idea  of  whole  and  part  is,  as  Sig\vart  points  out,  primar- 
ily the  idea  of  a  relation  in  space  —  i.e.,  of  a  larger  figure  or 
object  comprehending  or  containing  a  smaller;  but  in  many 
cases  the  idea  involves  also  the  notion  of  an  influence  exerted 
by  the  whole  upon  the  parts  or  by  the  parts  upon  the  whole. 
This  is  most  obvious  in  the  case  of  living  beings.  It  is 
because  I  can  control  the  movements  of  my  hand  and  feel  its 
injuries  that  it  seems  so  much  a  part  of  me — more  so  than 
my  hair  or  finger-nails.  Thus  the  idea  of  whole  and  part 
often  involves  both  dynamic  and  non-dynamic  relations. 

in  the  traditional  logic,  are  enumerated  near  the  beginning  of  the 
''Critique  of  Pure  Reason";  Mill's  are  given  in  I5k.  I.  Chap.  V,  of  his 
"Logic". 

Of  all  these  lists  Kant's  is  much  the  worst.  As  to  Mill's  Existence  and 
Non-existence,  we  shall  see  in  the  next  chapter  that  it  is  not  a  new  kind 
of  category  comparable  with  those  which  I  have  enumerated  ;  for  as 
Lotze  says,  "  to  exist  is  to  stand  related  ".  In  other  words,  'Existence' 
is  a  general  term  applied  to  whatever  has  any  of  the  particular  relations 
specified.  To  exist  and  to  have  a  place  in  the  world  of  related  things 
are  one  and  the  same. 


CERTAIN   COMBINED   RELATIONS.  85 

The  unity  of  an  animal  body  involves  also  the  relation  of 
means  and  end,  since  all  the  parts  cooperate. 

The  relation  of  Number  corresponds  closely  with  that  of 
whole  and  part.  Until  a  given  whole,  such  as  the  distance 
from  Cleveland  to  Buffalo,'  is  split  up  mentally  into  a  series  of 
parts  each  of  which  is  regarded  as  a  whole,  we  cannot  ex- 
press it  in  numbers,  e.g.,  61  leagues,  183  miles;  until  I  dis- 
tinguish between  the  units  in  'a  mass  of  humanity'  (as  the 
newspapers  sometimes  say)  or  in  a  flock  of  sheep  or  a  cloud 
of  dust,  I  cannot  count  them.  The  units,  of  course,  can  be 
chosen  perfectly  arbitrarily  :  leagues,  miles,  kilometers,  per- 
sons, couples,  families,  dozens,  pounds.  But  they  must  be 
similar  as  well  as  homogeneous  ;  I  cannot  add  persons  and 
miles,  and  if  I  wrish  to  add  leagues  and  kilometers  I  must 
reduce  one  to  the  other.  Having  settled  upon  our  similar 
units,  we  do  not  get  the  idea  of  any  definite  number  until  we 
count  them,  and  this  is  possible  only  when  they  are  so 
arranged  as  to  be  perceptible  separately,  that  is,  only  when 
they  are  a  certain  distance  apart  in  space,  like  dots  on  a 
page  or  the  sides  or  angles  of  a  figure  ;  or  in  time,  like  suc- 
cessive strokes  of  a  bell  or  throbs  of  pain. 

Thus  number,  like  whole  and  part,  is  primarily  a  relation 
of  space  or  time.  We  can  distinguish  a  triangle  from  a 
square  without  counting  the  sides,  because  they  do  not  look 
alike.  Similarly  any  single  object  looks  different  from 
a  group  of  two  or  more,  and  groups  of  two,  three,  and 
four  look  different  from  each  other.  Similarly  also  three 
strokes  of  a  bell  sound  different  from  one  or  two.  The 
higher  numbers  we  understand  largely  through  these  lower 
ones.  To  count  is  thus  to  tell  something  about  the  spatial 
or  temporal  appearance  the  objects  in  question  can  be  made 
to  present. 

All  propositions  are  divided  by  some  writers  into  pure  and 
modal.  Modal  propositions  contain  some  word  or  phrase  to 
intimate  "  the  degree  of  certainty  or  probability  with  which 
a  judgment  is  made  and  asserted"  (e.g. :  He  will  probably 


86      THE   RELATIONS   EXPRESSED    IN    PROPOSITIONS, 

come,  it  will  certainly  rain,  perhaps  he  is  here).  Pure  prop- 
ositions do  not.  Of  modal  propositions  we  shall  have  some- 
thing more  to  say.  For  the  present  we  may  regard  the 
modal  element  as  merely  noetic,  equivalent  to  some  such 
sentence  as  '  I  think  so  ',  'I  am  sure  of  it ',  'I  am  doubtful 
about  it  '. 

Some  writers  who  speak  of  modal  propositions  include  all 
those  which  contain  an  adverb,  e.g. :  '  He  acts  clumsily ',  '  he 
goes  quickly' .  Such  adverbs,  however,  are  mere  completions 
of  the  verb,  and  in  many  cases  they  can  be  avoided  altogether 
by  using  a  verb  which  already  contains  their  meaning,  e.g. : 
'  He  blunders  ',  '  he  hastens  '.  Whether  one  word  or  a  dozen 
is  necessary  to  tell  the  precise  relations  of  the  object  in  ques- 
tion is  a  mere  accident  of  language,  and  no  logical  distinction 
should  be  based  upon  it. 


CHAPTER   VII. 
WHAT   PROPOSITIONS   IMPLY   ABOUT   EXISTENCE.* 

WHEN  we  say  that  a  thing  is  green  or  large  or  terrible,  do 
we  necessarily  imply  that  it  t's,  or  exists?  To  put  the  ques- 
tion in  its  most  general  form,  does  the  copula  '  is  '  or  does 
any  proposition  imply  the  existence  of  the  things  whose  rela- 
tions it  affirms  or  denies  ? 

In  discussing  this  question  it  is  necessary  first  of  all  to  dis- 
tinguish between  the  subject  of  a  relation  and  what  is  named 
in  the  subject  of  a  sentence,  for  they  are  not  al-  Thetwo 
ways  identical.  It  is  thus  possible  to  believe  that  'subjects', 
every  relation  involves  the  existence  of  something  related 
without  being  forced  to  conclude  that  every  proposition  as- 
sumes the  existence  of  what  is  named  in  its  subject.  By  way 
of  illustration  let  us  quote  some  sentences  from  Keynes : 
"The  following  may  be  given  as  examples  of  universal 
propositions,  which  need  not  be  regarded  as  implying  the 
existence  of  their  subjects  :  No  unicorns  have  ever  been  seen  ; 
All  candidates  arriving  five  minutes  late  are  fined  one  shil- 
ling ;  Who  steals  my  purse  steals  trash ;  .  .  .  Every  body 
not  compelled  by  impressed  forces  to  change  its  state,  con- 
tinues in  a  state  of  rest  or  of  uniform  motion  in  a  straight 
line.  .  .  .  We  may  make  the  first  of  the  above  assertions 
without  intending  to  imply  that  unicorns  exist  unseen  ;  the 
second  does  not  commit  us  to  the  prophecy  that  any  candi- 

*  See  the  excellent  chapter  in  T.  N.  Keynes'  "Formal  Logic". 
Macmillan  &  Co. 

87 


88      WHAT   PROPOSITIONS   IMPLY    ABOUT   EXISTENCE. 

dates  will  arrive  five  minutes  late  ;  and  similarly  for  the  re- 
maining propositions."  * 

The  grammatical  subjects  of  these  propositions  are  the  terms 
'Unicorn',  'Candidates  arriving  five  minutes  late',  'He 
who  steals  my  purse  ',  and  '  Every  body  not  compelled  by 
impressed  forces  to  change  its  state',  and  Keynes  is  cer- 
tainly right  in  saying  that  the  propositions  in  question  do 
not  imply  the  existence  of  any  of  the  things  named  by  these 
terms. 

It  is  true,  nevertheless,  that  the  propositions  do  imply  the 
existence  of  something;  and  this  something  is  the  subject  of 
the  relations  expressed.  When  we  say  that  no  unicorns  have 
ever  been  seen  we  mean  that  no  human  being  has  ever  had 
the  experience  which  we  call  the  perception  of  a  unicorn, 
and  we  take  for  granted  the  existence  of  human  beings.  The 
statement  about  candidates  arriving  late  means  that  if  any 
one  should  appear  before  a  certain  board  as  a  candidate  but 
should  not  arrive  on  time,  he  would  be  fined.  It  assumes  the 
existence  of  the  members  of  the  board  and  of  persons  who 
may  wish  to  be  candidates,  and  points  out  certain  causal 
relations  which  may  arise  between  them.  lago's  words  do 
not  assume  the  existence  of  some  one  who  steals  his  purse  ; 
but  they  do  assume  the  existence  of  people  who  have  purses 
and  of  other  people  who  might  steal  them  if  they  could.  New- 
ton's law  of  motion  does  not  assume  the  existence  of  bodies 
not  acted  upon  from  without ;  but  it  does  assume  the  exist- 
ence of  material  bodies,  and  helps  to  explain  their  nature 
and  their  movements  by  telling  what  any  of  them  would  do 
if  they  were  not  acted  upon  from  without. 

Thus  when  we  distinguish  between  the  subjects  of  a  rela- 
tion and  the  things  denoted  by  the  subject  of  a  proposition, 
or,  better,  when  we  distinguish  between  the  things  we  are 
really  talking  about  and  the  things  that  the  structure  of  a  sen- 
tence sometimes  makes  us  seem  to  be  talking  about,  it  is  easy 

*  Pp.  201-2,  third  edition. 


DENIALS   OF   RELATIONS   AND   OF   EXISTENCE.        89 

enough  to  see  not  only  that  the  copula  'is',  but  that  every 
proposition,  regardless  of  the  copula,  implies  the  existence 
of  that  whose  relations  it  discusses. 

The  last  statement  holds  true  not  only  of  affirmative  but 
of  negative  propositions  and  even  of  those  in  which  there  is 
a  downright  denial  of  existence. 

Negative  propositions  as  such  are  easily  disposed  of.  When 
we  deny  that  a  thing  has  such  and  such  qualities  we  usually 
assume  that  it  exists  and  possesses  other  qualities 
incompatible  with  the  first.  If  any  one  should 
assert  that  John  Smith  was  not  good-natured  we  existence. 
might  assume  that  he  was  more  or  less  morose.  We  should 
usually  assume  that  he  did  exist.  Sometimes,  however,  we 
say  that  a  thing  has  not  certain  qualities  because  it  does  not 
exist  at  all ;  e.g. ,  '  A  snark  is  not  terrible  ';  '  ghosts  are  not 
to  be  feared'.  Here  the  negative  proposition  amounts  to 
one  in  which  existence  is  denied. 

But  even  when  we  say  that  something  does  not  exist,  our 
statement  is  really  one  concerning  what  does  exist.  To 
illustrate  what  I  mean  let  us  examine  a  peculiar  but  import- 
ant passage  in  Herbert  Spencer's  "First  Principles"  (Pt.  2, 
Chap.  4).  Mr.  Spencer  thinks  that  the  lately  discovered 
law  of  the  conservation  of  matter  is  one  which  no  rational 
being  ever  seriously  doubted,  even  though  he  supposed  him- 
self to  do  so.  He  bases  this  paradox  on  the  conviction 
that  nobody  can  possibly  succeed  in  thinking  of  nothing. 
Let  us  see  "what  happens",  says  Mr.  Spencer,  "when 
the  attempt  is  made  to  annihilate  matter  in  thought.  .  .  . 
Conceive  the  space  before  you  to  be  cleared  of  all  bodies 
save  one.  Now  imagine  the  remaining  one  not  to  be  re- 
moved from  its  place,  but  to  lapse  into  nothing  while  stand- 
ing in  that  place.  You  fail.  ...  It  is  impossible  to  think 
of  something  becoming  nothing,  for  the  same  reason  that  it 
is  impossible  to  think  of  nothing  becoming  something — the 
reason,  namely,  that  nothing  cannot  become  an  object  of 
consciousness." 


90      WHAT   PROPOSITIONS   IMPLY   ABOUT    EXISTENCE. 

From  this  argument  about  the  impossibility  of  thinking  of 
nothing,  Mr.  Spencer  believes  he  has  proved  that  no  one  can 
possibly  think  of  a  single  atom  of  matter  either  beginning  or 
ceasing  to  exist.  We  must  therefore,  according  to  the  argu- 
ment, think  of  the  world  and  every  atom  in  it  as  eternal, 
uncreated,  and  indestructible. 

Now,  I  believe  that  Mr.  Spencer  is  quite  right  in  saying 
that  we  cannot  think  of  nothing  (a  very  different  thing  from 
not  thinking  at  all).  Everything  we  imagine  or  think  of 
we  tend  to  think  of  as  existing,  and  as  long  as  our  thought  is 
concerned  wholly  with  any  given  object  we  cannot  possibly 
think,  though  through  force  of  habit  we  may  perhaps  speak, 
of  that  object  as  non-existent.  But  then  Mr.  Spencer  over- 
looked the  fact  that  when  we  assert  a  thing's  non-existence 
our  thought,  so  far  as  we  have  any,  is  a  thought,  not  of  the 
thing,  but  of  the  empty  background  where  the  thing  might 
have  been.  He  is  right  enough  in  saying  that  we  cannot  im- 
agine a  non-existent  body  as  non-existent,  but  we  certainly 
can  think,  whether  we  believe  it  or  not,  of  God  existing  in  a 
worldless  void  at  one  instant  and  with  worlds  about  him  at 
the  next,  or  of  a  universe  enriched  or  impoverished  by  the  ad- 
dition or  loss  of  some  speck  of  dust  or  of  some  whole  world. 
Certainly  every  child  has  seen  plants  grow  without  thinking 
of  the  nourishment  they  appropriate,  and  seen  them  burnt  up 
without  thinking  of  the  smoke  in  which  their  elements  are 
preserved. 

The  way  we  think  of  non-existence  is  well  illustrated  in 
the  nursery  rhyme  : 

Old  Mother  Hubbard 
Went  to  the  cupboard 

To  get  her  poor  dog  a  bone. 
But  when  she  got  there 
The  cupboard  'was  bare, 

And  so  the  poor  dog  got  none. 

A  bare  cupboard,  a  disappointed  woman,  and  a  hungry  dog  ! 
Here  is  a  vivid  picture  of  the  bone's  absence,  but  not  a  word 


THE   CONCEPTION   OF   REALITY.  91 

about  the  bone  itself!  Our  attention  is  turned  not  to  the 
bone,  but  to  the  empty  background.  "  As  for  man,  his 
days  are  as  grass  ;  as  a  flower  of  the  field,  so  he  flourisheth, 
for  the  wind  passeth  over  it  and  it  is  gone,  and  the  place 
thereof  shall  know  it  no  more.'1  Here  again  it  is  the  empty 
place,  not  the  grass  and  the  flower,  that  we  must  think  of  in 
order  to  get  the  full  sense  of  their  annihilation. 

To  say  that  a  thing  does  not  exist,  means  therefore  that 
the  world  or  whatever  other  reality  there  is  exists  without  it 
and  with  relations  other  than  those  which  its  presence  would 
have  involved. 

Thus  we  think,  not  of  what  is  not,  but  of  what  is  ;  and 
whatever  we  think  of,  we  think  of  as  existing  in  some  way  or 
other. 

This  whole  question  of  existence  can  be  made  clear  by 
tracing  the  origin  and  growth  of  the  distinction  between 

realities  and    illusions  or  fictions.     Young  chil- 

i          ,  •       ,  •     •        •  ~  The  con- 

dren    cannot    make    this    distinction.       Savages  ceptionof 

make  it  very  imperfectly,  and  even  adult  mem- 
bers of  a  civilized  society  often  fail  in  the  effort  to  apply  it. 

It  sometimes  happens  that  a  person  hears  his  name  called, 
looks  around,  can  see  nobody,  and  finally  concludes  that  the 
sound  was  imaginary.  At  first  the  sensation  of  sound  car- 
ried with  it  an  instinctive  belief  in  the  reality  of  something 
beyond  the  hearer  which  made  it.  Every  sensation  does 
this.  If  it  did  not  we  should  never  be  able  to  perceive 
//iings  at  all.  Instead  of  saying,  '  I  hear  some  one  speak',  '  I 
see  the  sun  ',  '  I  smell  a  rose  ',  '  I  feel  the  ground  ',  '  There  is 
a  mouse ';  we  should  only  be  able  to  say,  '  Lo,  a  feeling  like 
the  sound  of  words  !'  '  Lo,  a  vivid  sensation  of  sight !'  '  Lo, 
a  sweet  smell !'  '  Lo,  a  touch-feeling  !'  'Lo,  a  succession  of 
peculiar  visual  and  auditory  feelings  !' 

Thus  every  conception  of  reality  which  we  have  depends 
ultimately  upon  our  instinctive  tendency  to  interpret  feelings 
in  terms  of  things  acting  upon  us — to  say,  not  that  such  and 
such  a  feeling  is  now  going  on,  but  that  such  and  such  an 


92      WHAT   PROPOSITIONS   IMPLY   ABOUT   EXISTENCE. 

object  is  now  present.  From  this  tendency  to  objectify  our 
experience  we  can  never  wholly  escape. 

If  when  we  had  sensations  we  did  nothing  more  than  to 
refer  them  vaguely  to  something  or  other  acting  upon  us,  we 
should  never  be  able  to  detect  an  illusion.  As  a  matter  of 
fact  we  do  much  more,  for  we  build  up  as  soon  as  we  can  the 
concept'on  of  a  large  number  of  definite  objects,  acting  or 
disposed  to  act  in  definite  ways  upon  each  other  and  upon  us. 
We  learn  that  sounds  and  smells  come  from  objects  that  can 
be  seen  and  handled,  and  we  expect  floors  to  support  us, 
food  to  taste  good,  and  the  people  around  us  to  be  pleased  or 
annoyed,  as  the  case  may  be,  at  a  given  kind  of  conduct. 
We  gain,  in  short,  a  knowledge  of  the  nature  and  relations  of 
a  great  many  things.  Moreover,  we  expect  each  thing  to 
appear  and  act  at  one  time  as  it  did  under  similar  circum- 
stances at  another.  If  we  did  not,  there  would  be  no  mean- 
ing in  the  distinction  between  various  kinds  of  things. 

It  is  by  means  of  such  knowledge  of  things  and  the  way 
they  act  that  we  are  able  to  correct  our  first  impressions  and 
distinguish  between  that  which  we  have  experienced  and  that 
which  we  have  only  imagined.  If  we  hear  a  voice  but  see 
no  one,  we  conclude  that  we  were  mistaken  about  the  voice, 
because  it  is  easier  to  discredit  the  testimony  of  a  single  sense 
on  a  few  occasions  than  to  discredit  our  conviction  that  names 
are  not  called  in  the  absence  of  a  visible  and  tangible  person 
who  calls  them.  What  is  true  of  sensation  is  true  of  all 
thought.  What  we  think  about,  whether  it  be  an  ink-bottle 
or  a  dragon,  is  thought  about,  for  the  instant  at  least,  as 
though  it  were  real,  and  if  we  afterwards  deny  its  reality,  this 
is  because  our  thought  has  turned  from  the  object  itself  to  a 
wider  system  of  things  in  which  we  find  that  it  has  no  place. 

We  have  just  seen  how  we  conceive  of  every  object  of 
thought  as  real  until  we  find  that  it  will  not  fit  into  a  wider 
system  of  things.  The  ultimate  and  highest  test  of  individ- 
ual facts  would  be,  therefore,  a  thoroughly  consistent  and 
well-established  conception  of  the  whole  material  and  spirit- 


THE   CONCEPTION   OF   REALITY.  93 

ual  universe.  But  this  is  something  which  nobody  possesses. 
As  a  matter  of  fact  we  seldom  think  of  such  a  universe  at  all. 

Knowledge  comes  at  first  in  disconnected  patches.  These 
gradually  grow  together  and  are  combined  into  larger  fields. 
Within  each  field  our  conceptions  are  moderately  consis- 
tent, but  we  rarely  think  of  the  relations  between  various 
fields,  or  test  our  conceptions  of  one  by  comparing  it  with 
another.  Sunday  school  stories,  Greek  mythology,  German 
fairy  tales,  novels,  histories,  science,  theology:  these  are  all 
more  or  less  consistent  within  themselves  and  inconsistent 
with  each  other.  We  live  as  it  were  at  different  times  in 
different  worlds,  each  dominated  by  its  own  fundamental 
laws.  We  do  not  expect  to  find  cherubim  and  archangels 
on  Olympus  or  muses  "on  the  secret  top  of  Oreb  or  of 
Sinai  ",  nor  do  we  usually  think  of  Hamlet,  Solomon,  and 
Cinderella  meeting  together  beyond  the  Styx.  As  long  as 
we  keep  our  worlds  apart,  each  seems  real ;  the  more  vividly 
we  picture  it  the  more  real  it  seems ;  and  the  impression 
of  reality  lasts  until  we  compare  two  inconsistent  worlds 
together.  I  think  a  good  illustration  of  this  is  to  be  found 
in  Kipling's  story  of  "  Mowgli's  Brothers".  After  tell- 
ing how  a  little  naked  man -cub  toddled  into  a  wolfs  de:i 
and  was  adopted  by  Mother  Wolf,  the  author  explains  what 
Mother  and  Father  Wolf  must  do  in  order  to  have  the  adop- 
tion legally  recognized  and  ratified  by  the  Pack. 

' '  The  Law  of  the  Jungle  lays  down  very  clearly  that  any  wolf 
may,  when  he  marries,  withdraw  from  the  Pack  he  belongs 
to;  but  as  soon  as  his  cubs  are  old  enough  to  stand  on  their 
feet  he  must  bring  them  to  the  Pack  Council,  which  is  gen- 
erally held  once  a  month  at  full  moon,  in  order  that  the  other 
wolves  may  identify  them.  After  that  inspection  the  cubs 
are  free  to  run  where  they  please,  and  until  they  have  killed 
their  first  buck  no  excuse  is  accepted  if  a  grown  wolf  of  the 
Pack  kills  one  of  them.  The  punishment  is  death  where  the 
murderer  can  be  found,  and  if  you  will  think  for  a  minute 
you  will  see  that  this  must  be  so. ' ' 


94      WHAT   PROPOSITIONS   IMPLY   ABOUT   EXISTENCE. 

Now,  in  the  constitution  of  jungle  society  as  it  is  pic- 
tured in  the  story,  there  is  absolutely  no  reason  why  "this 
must  be  so  ",  and  so  when  we  "  think  fora  minute  "  we  have 
to  seek  for  the  reason  in  what  we  know  in  other  ways  of  wild 
beasts  and  their  habits;  and,  doing  this,  we  suddenly  see  the 
gap  between  the  every-day  world  and  the  world  of  Kipling's 
fancy,  and  realize  how  great  is  the  fiction  that  we  have  been 
treating  as  real. 

It  is,  of  course,  by  our  every-day  world,  the  world  of 
greatest  coherence  and  most  importance  for  us,  that  we  test 
all  others,  and  for  most  civilized  adults  nowadays  that  world 
is  the  world  of  physical  and  historical  science.  But  it  must 
not  be  forgotten  that  the  scientific  conception  of  the  world 
is  a  very  new  one.  In  the  middle  ages  the  every-day  world, 
the  world  of  greatest  coherence  and  most  importance,  was 
the  world  of  heaven  and  hell,  God  and  the  devil.  Beside 
it  the  earth  and  mundane  affairs  were  as  visions  and  empty 
dreams. 

By  history  we  test  the  truth  of  stories,  but  history  is  of 
more  recent  origin  than  physics.  It  is  one  great  story  con- 
sistent with  itself  and  with  physical  science  and  comprehend- 
ing and  explaining  as  many  shorter  stories  as  possible.  Be- 
fore it  was  told  the  truth  of  self-consistent  shorter  stories  or 
sets  of  stories  could  not  be  questioned.  Any  tale  seemed  as 
true  as  any  other  if  it  appealed  strongly  enough  to  the  im- 
agination and  emotions  of  the  hearer.  It  is  because  they 
know  little  science  and  history  that  children  and  savages  dis- 
tinguish between  truth  and  fiction  so  imperfectly. 

To  ask  whether  some  object  really  exists  or  whether  some 
story  is  true  implies  the  possession  of  some  accepted  system 
of  things  by  which  smaller  or  less  vital  systems  can  be  tested. 
If  a  smaller  system  is  found  to  agree  with  the  larger  a  de- 
liberate conviction  based  upon  this  agreement  is  added  to 
the  spontaneous  and  naive  conception  of  its  objects  as  real. 
The  objects  are  now  thought  of  as  real  in  a  new  and  deeper 
sense.  But  it  must  not  be  forgotten  that  the  distinction 


THE  CONCEPTION   OF   REALITY.  95 

between  the  two  kinds  of  reality  is  simply  one  of  degree,  and 
that  the  conception  of  the  reality  of  the  larger  system  of 
things  which  we  use  as  a  test  grows  itself  out  of  the  same 
spontaneous  tendency  to  objectify  our  impressions  that  ac- 
counts for  the  more  fragmentary  systems  which  we  have 
tested  by  means  of  it. 

When  we  discuss  the  nature  of  centaurs  and  dragons  we 
treat  these  creatures  as  real  in  the  sense  that  we  imagine  them 
before  us  with  perceptible  qualities  and  relations.  We  after- 
wards deny  their  reality  in  the  sense  that  we  seek  in  vain  to 
find  a  place  for  them  in  the  wider  scheme  of  consistently  re- 
lated things  which  we  have  come  to  regard  as  alone  of  vital 
interest.  Unless  we  took  the  wider  system  of  things  for 
granted  we  could  not  test  the  narrower.  Thus  to  deny  the 
existence  of  one  thing  is  really  to  say  something  about  the 
relations  of  some  wider  or  more  certain  universe  whose 
existence  we  assume  ;  and  thus  every  proposition,  whether  its 
copula  is  some  part  of  the  verb  'to  be '  or  whether  it  is  some- 
thing else,  implies  the  existence  of  something,  though  not 
necessarily  of  the  object  described  in  its  subject. 


CHAPTER  VIII. 
THE    FORMAL   CHARACTERISTICS   OF    PROPOSITIONS. 

IN  every  proposition  something  is  either  asserted  or  denied 

of  a  given  object  more  or  less  definitely  pointed  out.      When 

something  is  asserted   the    proposition    is  called 

and  affirmative  (e.g.,    'Dogs  like  meat',    'Iron  is   a 

metal'),  when  denied,    negative  (e.g.,  'Dogs  do 

not  like  meat ',  '  Iron  is  not  a  metal ').      The  character  of  a 

proposition  as  affirmative  or  negative  is  called  its  quality. 

When  a  proposition  states  something  about  some  one  defi- 
nitely designated  object  it  is  called  singular,  e.g.,  'Socrates 
was  flat-faced  ',  '  My  dog  is  not  savage  ',  '  The  last  man  in 
the  row  is  my  cousin  '. 

When  it  states  something  about  every  member  of  a  desig- 
nated group  of  objects  it  is  called  universal,  e.g.,  '  All  men  are 
mortal',  'No  Spanish-American  state  has  a  stable  govern- 
ment ',  '  Every  event  has  a  cause  '. 

When  it  states  something  about  some  undesignated  or  im- 
perfectly designated  member  or  members  of  a  given  group  of 
objects  it  is  called  particular,  e.g.,  'Some  of  the  American 
races  were  highly  civilized',  '  One  of  the  men  in  the  row  is 
my  cousin  ',  '  Some  dogs  are  not  savage',  '  A  certain  man  had 
two  sons  '. 

The  term  '  particular '  is  here  used  in  a  peculiar  sense, 
quite  contrary  to  its  ordinary  meaning,  for  particular  prop- 
ositions are  the  only  ones  which  do  not  give  information 
about  particular  or  definitely  designated  objects.  If  a  gen- 


QUALITY   AND   QUANTITY.  97 

eral  tells  his  officers  that'  one  of  them  has  blundered,  each 
can  ask  :  Do  you  mean  me  ?  But  if  he  uses  a  singular  prop- 
osition and  s:iys  that  Captain  Jones  has  blundered,  or  a 
universal  and  says  that  they  have  all  blundered,  the  question 
is  no  longer  possible.  The  term  '  particular  '  as  used  in  logic 
is  derived  directly  from  the  Latin  parlicula,  a  particle,  and 
has  been  applied  to  certain  propositions  merely  because, 
unlike  universals,  they  refer  to  only  part  of  the  class  or  group, 
of  objects  mentioned. 

Singular  propositions  are  usually  classified  with  universals 
because  they  point  out  the  object  spoken  of  in  the  same 
definite  way,  and  because  for  most  logical  purposes  definite- 
ness  of  reference  is  much  more  important  than  the  number 
of  objects  to  which  we  refer.* 

The  character  of  a  proposition  as  universal,  singular,  or 
particular  is  called  its  quantity, 

If  we  neglect  singular  propositions  and  consider  the  various 
combinations  of  quantity  and  quality  in  universals  and  par- 
ticulars there  are  four  kinds  of  propositions,  each  of  which 
it  is  customary  to  denote  by  one  of  the  following  symbols : 

A.   Universal  affirmative,  as  '  All  S's  are  P'. 

E.   Universal  negative,  as  '  No  S  is  P '. 

I.     Particular  affirmative,  as  '  Some  S's  are  P  '. 

O.    Particular  negative,  as  '  Some  S's  are  not  P  '. 

The  symbols  A  and  I  are  respectively  the  first  and  the 
second  vowels  in  the  word  affirmo.  E  and  O  belong  in  the 
same  way  to  nego. 

The  reader  should  notice  that  the  proposition  '  All  S's  are 

*  This  is  the  real  reason;  but  it  is  not  always  the  reason  given. 
Whately,  for  example,  says  that  singular  propositions  are  to  be  treated 
as  universals,  because  they  tell  something  '  about  the  whole  of  the  sub- 
ject '.  When,  for  example,  we  say  that  Brutus  killed  Cresar,  we  are 
speaking  about  the  whole  of  Brutus.  This  is  of  course  absurd.  \Ve 
should  speak  just  as  much  about  the  whole  of  Brutus  if  we  said  that  a 
certain  Roman  killed  Caesar.  It  is  not  a  question  of  how  much?  but  of 
who  ?  or  which  ? 


98      FORMAL   CHARACTERISTICS   OF   PROPOSITIONS. 

not  P'  usually  means  'It  is  not  true  that  all  S's  are  P ',  i.e. , 
'Not  all  S's  are  P'    or  '  Some  S's  are   not  P'. 

Ambiguities    ,..,.„  „        ,,,,  1-1 

of  quantity  It  is  therefore  O,  not  t,.  \\hen  we  realize  that 
or  quality.  .  r  ,  .  .  . 

expressions    of    this    sort    are     ambiguous     we 

should  try  hard  to  avoid  using  them.  When  we  find 
them  used  by  others  who  may  not  have  recognized  their 
ambiguity  we  should  try  to  interpret  them  according  to  the 
real  meaning  of  the  speaker — if  he  had  a  definite  meaning 
— and  not  according  to  any  arbitrary  rule.  If  it  is  im- 
possible to  tell  what  his  real  meaning  is,  we  should  make 
it  plain  that  this  is  the  case.  The  one  thing  that  we 
should  certainly  not  do  is  to  allow  such  expressions  to  pass 
without  question.  If  we  do  so  they  are  likely  to  be  taken  in 
one  sense  at  one  time  and  in  another  at  another ;  and  thus 
to  lead  us  to  conclusions  which  we  really  have  no  right  to 
reach  or  to  disputes  for  which  there  was  really  no  occasion. 

The  word  '  few ',  as  Jevons  has  pointed  out,  must  be  inter- 
preted with  care  ;  "  for  if  I  say  '  few  books  are  at  once  learned 
and  amusing  ',  I  may  fairly  be  taken  to  assert  that  a  few  books 
certainly  are  so,  but  what  I  really  mean  to  draw  attention  to 
•is  my  belief  that  '  the  greater  number  of  books  are  not  at  once 
learned  and  amusing.'  A  proposition  of  this  class  is  gener- 
ally to  be  classed  rather  as  O  than  I  ".* 

Whether  the  word  some  means  some  but  not  all  or  at  least 
some,  perhaps  all,  depends  largely  upon  the  scientific  training 
of  the  speaker.  Like  the  fish  that  bites  at  every  wriggling  ob- 
ject and  the  baby  that  grasps  everything  within  its  reach  re- 
gardless of  possible  burns  or  cuts,  we  all  tend  to  generalize 
too  carelessly.  When  a  confiding  boy  leaves  home  he  is 
likely  to  take  it  for  granted  that  every  one  is  trustworthy — 
proposition  A  ;  because  of  his  credulity  he  is  soon  cheated, 
and  then  like  David  in  his  wrath  he  may  say  that  all  men 
are  liars,  i.e.,  that  no  one  is  trustworthy  —  proposition  E. 
Soon,  however,  he  gets  a  letter  from  home  or  is  befriended 

*  "  Elementary  Lessons  in  Logic  ",  p.  67. 


UNDES1GNATED   QUANTITY   OR   QUALITY.  99 

by  an  old  acquaintance  and  he  qualifies  his  sweeping  con- 
demnation. "Some  people  are  trustworthy",  he  now  says, 
implying  that  all  but  a  chosen  few  are  unreliable.  After  a 
while,  however,  he  learns  the  value  of  cautious  statements, 
and  if  he  should  then  go  to  a  new  place  and  be  fortunate 
in  his  first  acquaintances  he  might  say  "  Some  people  here 
are  trustworthy",  implying  nothing  whatever  about  the  rest 
except,  perhaps,  that  he  did  not  know  them. 

In  short,  the  development  of  particular  propositions  is  a 
mark  of  increasing  caution  and  accuracy.  The  end  which 
they  serve  is  therefore  defeated,  at  least  in  part,  when  they 
are  understood  to  imply  more  than  they  state.  Often  they 
do  imply  more  —  but  merely  because  a  speaker  or  hearer  is 
not  yet  sufficiently  well  trained  to  realize  that  a  qualified 
statement  can  be  made  on  general  principles.  Here  again 
one  must  take  care  to  speak  in  such  a  way  as  to  be  under- 
stood aright  by  his  hearers  (whoever  they  may  be),  and  to 
try  and  find  a  definite  interpretation  for  the  statements  of 
others  which  they  themselves  would  accept. 

Instead  of  being  ambiguous,  words  used  to  denote  quan- 
tity and  quality  are  often  lacking  altogether. 


Sometimes  the  meaning  is  clear  enough  without  Quantity  or 
them;  but  sometimes  it  is  not. 

The  term  indefinite,  indesignate,  or  premdesignaieis,  applied 
to  propositions  whose  form  does  not  show  whether  they  are 
intended  to  be  universals  or  particulars.  When,  for  exam- 
ple, we  say  that  dogs  delight  to  bark  and  bite,  or  that 
republics  are  more  free  than  monarchies,  or  that  crows  are 
black,  do  we  mean  the  statement  to  apply  to  every  dog, 
every  republic,  every  crow,  or  only  to  some  larger  or  smaller 
number  of  them  ?  Indefinite  propositions  must  not  be  con- 
fused with  particulars.  The  quantity  of  a  particular  proposi- 
tion is  perfectly  clear,  but  the  object  to  which  it  refers  is  not 
definitely  designated.  The  quantity  of  an  indefinite  proposi- 
tion, on  the  other  hand,  is  not  clear,  and  for  that  reason  it 
is  impossible  to  say  whether  it  is  meant  to  refer  to  any 


loo   FORMAL   CHARACTERISTICS   OF   PROPOSITIONS. 

definitely  designated  objects  or  not.  Particular  propositions 
are  indefinite  in  their  reference;  indefinite  propositions, 
ambiguous. 

When  the  form  of  a  proposition  gives  no  indication  of  its 
quantity  it  is  very  easy  to  accept  it  or  prove  it  true  when 
interpreted  as  a  particular  and  then  use  it  as  though  it  were 
true  as  a  universal.  Here  is  an  example:  "Improbable 
events  happen  almost  every  day;  events  which  happen  almost 
every  day  are  probable  events;  therefore  improbable  events 
are  probable  events."  When  the  first  premise  of  this 
argument  is  assumed  to  be  true  it  is  evidently  understood 
to  mean  that  some  improbable  event  or  other  happens  almost 
every  day;  and  from  it  in  conjunction  with  the  other 
premise  we  have  the  right  to  conclude  that  the  occurrence 
of  some  improbable  event  or  other  is  probable,  but  nothing 
more.  When  the  premise  is  understood  in  this  sense 
throughout  it  certainly  will  not  help  us  to  conclude  that 
improbable  events  are  probable  events.  It  is  capable,  how- 
ever, of  being  interpreted  to  mean  that  every  improbable 
event  happens  almost  every  day;  and  when  taken  in  this 
latter  sense  it  certainly  will  help  us  to  reach  the  conclusion. 
Every  improbable  event  happens  almost  every  day;  events 
which  happen  almost  every  day  are  probable  events;  there- 
fore every  improbable  event  is  a  probable  event.  But,  then, 
when  the  premise  is  understood  in  this  sense  nobody  would 
admit  its  truth. 

\Ve  must  not  assume,  however,  that  the  quantity  or  qual- 
ity of  a  proposition  has  not  been  indicated  merely  because  it 
has  riot  been  expressed  formally  by  one  of  the  words  '  some  ', 
'  all  ',  '  none',  '  not '.  Minto  puts  the  matter  as  follows: 

'  The  expression  of  Quantity,  that  is,  of  universality  or 
non-universality,  is  all-important  in  syllogistic  formulae.  In 
them  universality  is  expressed  by  all  or  none.  In  ordinary 
speech  universality  is  expressed  in  various  forms,  concrete 
and  abstract,  plain  and  figurative,  without  the  use  of  '  all  ' 
or  '  none  '. 


UNDESIGNATED   QUANTITY   OR   QUALITY.  101 

Uneasy  lies  the  head  that  wears  a  crown. 

He  can't  be  wrong  whose  life  is  in  the  right. 

What  cat's  averse  to  fish  ? 

Can  the  leopard  change  his  spots  ? 

The  longest  road  has  an  end. 

Suspicion  ever  haunts  the  guilty  mind. 

Irresolution  is  always  a  sign  of  weakness. 

Treason  never  prospers. 

****** 

"All  the  above  propositions  are  '  Pre-designate '  [i.e., 
definite]  universals,  and  reducible  to  the  form  All  S  is  P,  or 
No  S  is  P. 

"The  following  propositions  are  no  less  definitely  par- 
ticular, reducible  to  the  form  I  or  O  [i.e.,  Some  S  is  P,  or 
Some  S  is  not  P].  In  them,  as  in  the  preceding,  quantity 
is  formally  expressed,  though  the  forms  used  are  not  the 
artificial  syllogistic  forms: 

Afflictions  are  often  salutary. 
Not  every  advice  is  a  safe  one. 
All  that  glitters  is  not  gold. 
Rivers  generally  run  into  the  sea. 

"  Often,  however,  it  is  really  uncertain  from  the  form  of 
common  speech  whether  it  is  intended  to  express  a  universal 
or  a  particular.  The  quantity  is  not  formally  expressed. 
This  is  especially  the  case  with  proverbs  and  loose  floating 
sayings  of  a  general  tendency.  For  example : 

Haste  makes  waste. 

Knowledge  is  power. 

Light  come,  light  go. 

Left-handed  men  are  awkward  antagonists. 

Veteran  soldiers  are  the  steadiest  in  fight. 

"  Such  sayings  are  in  actual  speech  for  the  most  part 
delivered  as  universals.  It  is  a  useful  exercise  of  the  Socratic 
kind  to  decide  whether  they  are  really  so.  This  can  only 


102   FORMAL   CHARACTERISTICS   OF   PROPOSITIONS. 

be  determined  by  a  survey  of  facts.  The  best  method  of 
conducting  such  a  survey  is  probably  (i)  to  pick  out  the 
concrete  subject,  '  hasty  actions  ',  '  men  possessed  of  knowl- 
edge ',  '  things  lightly  acquired  ' ;  (2)  to  fix  the  attribute  or 
attributes  predicated;  (3)  to  run  over  the  individuals  of  the 
subject  class  and  settle  whether  the  attribute  is  as  a  matter 
of  fact  meant  to  be  predicated  of  each  and  every  one. 

"This  is  the  operation  of  Induction.  If  one  individual 
can  be  found  of  whom  the  attribute  is  not  meant  to  be 
predicated,  the  proposition  is  not  intended  as  universal. 

"  Mark  the  difference  between  settling  what  is  intended 
and  settling  what  is  true.  .  .  . 

"The  bare  forms  of  Syllogistic  are  a  useless  item  of 
knowledge,  unless  they  are  applied  to  concrete  thought. 
And  determining  the  quantity  of  a  common  aphorism  or 
saw,  the  limits  within  which  it  is  meant  to  hold  good,  is  a 
valuable  discipline  in  exactness  of  understanding."  * 

When  the  function  of  a  proposition  is,  not  to  describe 
some  one  object  or  set  of  objects,  but  to  tell  of  a  causal  or 
Double  other  relation  which  exisls  between  several  (e.g., 

Quantity.  jo}in  strikes  James;  David  defeated  the  Philis- 
tines), it  is  rather  arbitrary  to  determine  the  quantity  of  the 
proposition  with  reference  merely  to  what  happens  to  be 
named  in  the  subject.  It  would  be  fairer  to  recognize  both 
parties  to  the  relation,  and  to  determine  the  quantity  of  the 
proposition  with  reference  to  each.  '  Each  of  these  hunters 
shot  a  bird  '  is  a  universal  proposition  with  reference  to  the 
hunters,  but  particular  with  reference  to  the  birds.  '  Almost 
any  Turk  hates  a  Greek  '  is  particular  with  reference  to  the 
Turks,  universal  with  reference  to  the  Greeks.  '  All  Turks 
and  Greeks  hate  each  other  '  is  universal  with  reference  to 
both.  '  There  are  many  thieves  in  the  land  '  is  particular 
with  reference  to  the  thieves,  singular  with  reference  to  the 
land. 

*  William  Minto,  "Logic,  Inductive  and  Deductive",  Scribners, 
1895,  pp.  70-73. 


EXCLUSIVES  AND   EXCEPTIVES.  103 

Let  it  be  remembered,  therefore,  that  though  it  may 
sometimes  be  convenient  to  describe  the  quantity  of  such  a 
proposition  with  reference  to  only  one  of  the  related  parties, 
such  a  description  is  both  arbitrary  and  incomplete. 

There  are  two  closely  allied  kinds  of  propositions,  much 
harder  to  define  than  to  deal  with  in  practice,  called  respec- 
tively exceptive  and  exclusive.  The  subject  of 

....  .  .....  .  Exclusives 

each  kind  contains  some  such  limiting  phrase  as  and 

z    /         ?        r  j         ^u-  ,.    exceptives. 

none  but,  only,  alone,  except ;  and  on  this  account 

they  are  often  confused,  in  spite  of  a  real  contrast  between 
them. 

Exceptive  propositions  state  that  something  is  true  of  all 
the  members  of  a  given  group  of  objects  except  those  speci- 
fied. Exclusive  propositions,  on  the  other  hand,  state  that 
something  is  true  of  certain  specified  members  of  a  group 
only. 

Here  are  some  examples  of  the  two: 

Exceptive  affirmative:  All  but  the  Germans  departed. 
Exclusive  :  The  Germans  alone  departed. 

Exceptive  negative:       No  one  but  the  Germans  departed. 
Exclusive       "         :       The  Germans  alone  did  not  depart. 

Exceptive  affirmative:  All  but  the  brave  deserve  the  fair. 
Exclusive  :  The  brave  alone  deserve  the  fair. 

Exceptive  negative:       None  but  the  brave  deserve  the  fair. 
Exclusive       "         :       The  brave  are  the  only  ones  who  do 
not  deserve  the  fair. 

It  will  be  noticed  that  each  kind  of  proposition  can  be 
either  affirmative  or  negative,*  and  that  the  exclusive  affir- 

*  The  fact  that  each  kind  of  proposition  can  be  either  affirmative  or 
negative  is  overlooked  in  some  of  the  text-books.  Jevons,  for  example, 
assumes  in  the  following  definitions  that  both  kinds  must  be  affirmative: 
"Exceptive  propositions  affirm  a  predicate  of  all  the  subject  with  the 
exception  of  certain  defined  cases,  to  which,  as  is  implied,  the  predicate 
does  not  belong."  "Exclusive  propositions  contain  some  words,  such  as 
only,  alone,  none  but,  which  limit  the  predicate  to  the  subject."  Where 
a  predicate  is  '  limited  to  a  subject ',  it  is  certainly  affirmed  and  not 


104   FORMAL   CHARACTERISTICS   OF   PROPOSITIONS. 

mative  has  the  same  meaning  as  the  exceptive  negative,  and 
v ice  versa. 

In  the  first  set  of  examples  above  given  there  can  be  no 
doubt  about  the  meaning:  in  each  case  we  are  told  that  the 
Germans  did  one  thing  and  that  the  others  did  the  other. 
In  the  second  set,  however,  the  meaning  is  not  so  clear. 
When  we  say  that  all  but  the  brave  deserve  the  fair,  or,  to 
make  the  example  less  unnatural,  all  but  the  brave  deserve 
to  die,  or  that  the  brave  are  the  only  ones  who  do  not 
deserve  to  die,  do  we  mean  that  every  brave  man  deserves 
to  live,  or  merely  that  so  far  as  courage  is  concerned,  brave 
men  do  not  deserve  death  ?  In  the  latter  case  a  brave  man 
might  deserve  it  on  other  grounds.  So  when  we  say  that 

denied  of  the  subject.  Both  definitions  thus  assume  that  the  propositions 
arc  affirmative.  As  examples  of  exclusive  propositions  Jevons  gives 
"Elements  alone  are  metals"  and  "None  but  elements  are  metals". 
He  states  that  they  are  equivalent  and  assumes  that  they  are  both 
affirmative.  As  an  example  of  exceptive  piopositions  he  gives  "All  the 
planets  except  Venus  and  Mercury  are  beyond  the  earth's  orbit  ".  But 
suppose  that  instead  of  affirming  this  we  should  deny  all  the  facts  as- 
serted, the  proposition  would  then  read  :  None  of  the  planets  except 
Venus  and  Mercury  are  beyond  the  earth's  orbit.  This  form  is  pre- 
cisely identical  with  "  None  but  elements  are  metals",  which  Jevons 
regards  as  an  affirmative  exclusive  proposition.  The  form  is  clearly  ex- 
ceptive and  clearly  negative,  and  there  is  no  reason  why  the  proposi- 
tion should  be  regarded  as  either  exclusive  or  affirmative,  unless  the 
distinction  between  the  two  kinds  of  proposition  is  alxjlished  altogether. 
This  is  actually  done  by  Minto,  as  follows  :  "  The  formula  for  EXCLUSIVE 
PROPOSITIONS.  '  None  but  the  brave  deserve  the  fair'  ;  '  No  admittance 
except  on  business'  ;  '  Oidy  Protestants  can  sit  on  the  throne  of  Eng- 
land'. These  propositions  exemplify  different  ways  in  common  speech 
of  naming  a  subject  exclusively,  the  predication  being  made  of  all  outside 
a  certain  term."  (P.  76.)  The  trouble  with  this  description  is  that 
where  the  subject  is  'named  exclusively',  as  in  the  example  about 
Protestants,  the  predication  as  it  stands  is  not  made  about  -all  outside 
the  term',  but  about  those  inside  it.  On  the  other  hand,  when  the 
predication  is  made  about  'all  outside  the  term  '  as  in  the  two  other  ex- 
amples, the  subject  is  not  '  named  exclusively  '  ;  for  that  which  is  named 
is  not  the  subject. 


EXCLUSIVES   AND   EXCEPTIVES.  105 

the  brave  alone  deserve  the  fair  or  that  none  but  the  brave 
deserve  the  fair,  do  we  mean  that  every  brave  man  deserves 
a  fair  wife  no  matter  what  he  may  be  in  other  respects,  or 
merely  that  to  deserve  one  he  must  at  least  be  brave  ? 

The  first  set  of  propositions  are  unambiguous  because  they 
are  purely  historical  statements  about  certain  individuals  as 
such.  The  second  are  ambiguous  because  they  express 
conditions  about  kinds  of  objects  and  they  do  not  make  it 
plain  whether  the  condition  mentioned  is  or  is  not  the  only 
one  upon  which  the  case  depends.* 

*  Exclusive  and  exceptive  propositions  can  be  varied  a  good  deal  in 
quantity.  When  we  say  The  Germans  alone  remained  we  (i)  specify 
clearly  the  smaller  group  (of  Germans  as  distinguished  from  the  rest  of 
the  persons  involved,  and  (za)  say  something  about  each  member  of  the 
specified  smaller  group  (they  remained)  and  (2b)  about  each  of  the  rest 
(they  did  not  remain).  The  proposition  is  thus  in  every  possible  respect 
universal. 

When  we  say  The  brave  alone  deserve  the  fair,  we  (i)  distinguish 
clearly  enough  between  our  groups,  (2b)  we  say  something  about  all 
who  are  not  brave,  and  (2d)  if  we  are  interpreted  as  saying  anything 
at  all  about  those  who  are  brave, — namely,  that  they  have  complied  with 
one  condition — we  say  it  about  all  of  them.  This  proposition  is  thus 
also  universal  in  every  respect. 

When  we  say  Some  of  the  Germans  were  the  only  persons  who  re- 
mained, we  still  (i)  specify  the  smaller  group  clearly  and  (23)  still  say 
something  about  all  the  persons  outside  of  it  ;  but  (2a)  the  individuals 
within  it  of  whom  we  speak  are  no  longer  definitely  designated.  The 
proposition  is  thus  in  one  respect  particular.  When  we  say  The  Ger- 
mans and  some  others  alone  remained,  I  is  still  definite,  2a  is  universal, 
and  2b  particular.  When  we  say  Some  of  the  Germans  and  some  of 
the  others  alone  remained,  the  groups  are  still  clearly  distinguished,  but 
the  original  proposition  is  broken  up  into  two  exclusives,  each  particular 
in  so  far  as  it  fails  to  specify  the  distinction  between  those  who  did  and 
those  who  did  not  stay.  Each  of  these  exclusives  is  equivalent  to  both 
I  and  O  :  some  stayed  and  some  did  not. 

When  we  say  The  soldiers  of  one  nation  alone  remained,  a  statement 
is  made  (2)  about  each  member  of  each  group.  To  this  extent  the 
proposition  is  universal.  But  as  (1)  the  smaller  group  is  no  longer  defi- 
nitely specified,  the  proposition  is  in  this  respect  particular. 

The  precise  meaning  as  to  quantity  of  an'  exclusive  or  exceptive 
proposition,  like  that  of  any  other,  may  be  indefinite. 


106   FORMAL   CHARACTERISTICS   OF   PROPOSITIONS. 

So  far  we  have  been  dealing  with  what  are  called  categori- 
cal propositions;  those  in  which  something  is,  or  at  least 
seems  from  the  form  of  the  proposition  to  be, 
and  Hypo-  stated  without  alternative  and  without  condi- 
tion. Propositions  in  which  it  is  affirmed  that 
one  or  other  of  several  alternative  states  of  affairs  exists  are 
called  disjunctive  or  alternative,  e.g.,  Every  man  is  either 
married  or  single;  He  is  either  a  fool  or  a  knave;  Either  he 
is  a  knave  or  I  have  been  grossly  deceived ;  Either  A  or  B 
did  it;  He  is  either  not  here  or  not  there.*  Propositions  in 
which  it  is  affirmed  that  if  some  specified  state  of  affairs 
exists  another  specified  state  of  affairs  also  exists  are  called 
hypothetical, \  e.g.,  If  he  is  not  a  fool  he  is  a  knave;  If  he  is 
a  knave  I  have  been  grossly  deceived;  If  he  is  not  in  the 
room  he  is  not  in  the  house. 

The  part  of  a  hypothetical  proposition  which  specifies  the 
condition,  either  of  something  being  so,  or  of  our  knowing 
it,  is  called  the  antecedent,  the  part  which  specifies  what 
follows  from  that  condition  is  called  the  consequent. 

Disjunctive  propositions  state  that  one  of  two  things  must 
be  true;  but  do  they  imply  that  both  cannot  be  true  ?  This 
question  has  been  discussed  at  much  length.  If  a  man  is 
married  he  cannot  possibly  be  single.  We  know  this  from 
the  nature  of  things,  but  there  is  no  reason  in  the  nature  of 

*  A  negative  proposition  asserts  the  existence  of  a  state  of  affairs  just 
as  much  as  an  affirmative. 

•f  "  This  is  the  familiar  form  of  the  disjunctive  judgment.  ...  It  is 
usual  to  mention  along  with  it  the  copulative  judgment  ('S  is  both  p 
and  q  and  r '),  and  the  remotlve  judgment  ( '  S  is  neither  p  nor  q  nor  r '  -,; 
but  in  spite  of  the  external  analogy  of  form,  neither  of  these  has  the 
same  logical  value  as  the  disjunctive  ;  the  first  is  only  a  collection  of 
positive,  the  second  of  negative,  judgments  with  the  same  subject  and 
different  predicates,  which  latter  are  not  placed  in  any  logically  im- 
portant relation  to  each  other.  The  disjunctive  judgment  alone  ex- 
presses a  special  relation  between  its  members  :  it  gives  its  subject  no 
predicate  at  all,  but  prescribes  to  it  the  alternative  between  a  definite 
number  of  different  predicates."  Lotze,  "Logic",  §  69.  (Clarendon 
Press.) 


DISJUNCTIVES   AND   HYPOTHETICALS.  107 

things  why  a  person  cannot  be  both  fool  and  knave.  When 
it  is  asserted  that  he  is  either  one  or  the  other,  is  it  neces- 
sarily implied  by  the  form  of  the  statement  that  he  is  not 
both  ?  Fowler  says:  "  It  seems  to  me  that  in  the  expression 
'either  --or  — '  we  distinctly  exclude  the  possibility  of 
both  alternatives  being  true,  as  well  as  of  both  being  false. 
In  fact,  when  we  do  not  wish  to  exclude  the  possibility  of 
both  being  true,  we  add  the  words  '  or  both  ',  thus:  '  He  is 
either  a  fool  or  a  knave,  or  both  ' ;  '  I  shall  come  either 
to-day  or  to-morrrow,  or  perhaps  both  days'."  *  With  this 
view  Thomas  Aquinas,  Kant,  Hamilton,  Boole,  Bradley, 
and  others  agree.  Whately,  Mansel,  Mill,  Jevons,  Keynes,  f 
and  others  maintain  on  the  other  hand  that  such  proposi- 
tions merely  mean  that  both  alternatives  cannot  be  false, 
though  both  may  be  true.  Says  Keynes:  "  Suppose  it  laid 
down  as  a  condition  of  eligibility  for  some  appointment  that 
every  candidate  must  be  a  member  either  of  the  University 
of  Oxford,  or  of  the  University  of  Cambridge,  or  of  the 
University  of  London.  Would  any  one  regard  this  as  imply- 
ing the  ineligibility  of  persons  who  happened  to  be  members 
of  more  than  one  of  these  universities  ? ' ' 

The  question  is,  of  course,  one  of  the  interpretation  of 
language,^ not  of  logical  processes.  So  far  as  logic  is  con- 
CerrTeaany  one  is  at  liberty  to  use  language  in  any  sense  he 
pleases,  provided  that  he  explains  beforehand  the  sense  in 
which  he  means  to  use  it ;  but  since  there  is  a  real  difference 
in  usage~Tt  seems  to  me  better  in  this  case,  as  in  the  case  of 
the  word  '  some ',  to  assume  that  the  words  are  used  with  the 
greatest  Qaution  and  imply  nothing  but  what  is  stated.  Let 
us,  therefore,  agree,  at  least  for  the  purposes  of  this  book, 
that  when  we  say  that  one  or  other  of  several  alternatives  is 
true  we  do  not  necessarily  imply  that  both  cannot  be  true, 
though  of  course  we  do  imply  that  both  cannot  be  false. 

*  "Deductive  Logic  ",  p.  n8.  Ninth  Ed.  (Clarendon  Press). 
•}•  See  Jevons,  "Principles  of  Science  ",  p.  68,  and  Keynes,  "Formal 
Logic  ",  §  140. 


lo8   FORMAL   CHARACTERISTICS   OF   PROPOSITIONS. 

Like  exclusive  and  exceptive  propositions,  hypothetical 
and  disjunctive  propositions  are  different  in  form  and  must 
be  distinguished  from  each  other,  though  they  can  be  made 
to  express  the  same  meaning.  The  following  table  shows 
the  relations  between  them : 

Disjunctive.  Hypothetical. 

A  is  either  B  or  C  =  If  A  is  not  B,  it  is  C. 

=  If  A  is  not  C,  it  is  B. 
A  is  either  not  B  or  not  C  •=.  If  A  is  B,  it  is  not  C. 

— .  If  A  is  C,  it  is  not  B. 
A  is  either  B  or  not  C  —  If  A  is  not  B,  it  is  not  C. 

=  If  A  is  C,  it  is  B. 

In  each  case  there  are  two  hypothetical  propositions, 
either  of  which  is  equivalent  to  the  disjunctive,  and  each  of 
which  is  exactly  equivalent  to  the  other.  To  say  If  A  is  not 
B  it  is  C  means  precisely  the  same  thing  as  to  say  If  A  is  not 
C  it  is  B;  and  so  with  the  rest. 

If  any  one  were  asked  the  use  of  disjunctive  and  hypo- 
thetical propositions,  the  first  answer  that  occurred  to  him 
would  probably  be:  To  express  knowledge  combined  with 
doubt.  To  use  Venn's  illustration,  if  I  say  that  A.B.  is 
either  a  barrister  or  a  solicitor,  I  express  my  knowledge  that 
he  is  a  lawyer  and  my  doubt  as  to  his  precise  standing  at 
the  bar.  The  same  thought  would  be  expressed  in  the 
hypothetical  proposition,  '  If  he  is  not  a  barrister  he  is  a 
solicitor '. 

But  disjunctive  and  hypothetical  propositions  are  not 
always  used  to  express  doubt.  When,  for  example,  we  say 
that  in  the  United  States  every  person  is  either  married  or 
single,  the  statement  does  not  express  the  slightest  doubt  as 
to  the  condition  of  any  given  individual  in  this  respect.  Its 
real  force  is  to  explain  the  laws  or  social  customs  of  the 
country,  under  which  a  person  is  regarded  as  single  until 
some  prescribed  condition  has  been  fulfilled,  and  then  as 
married.  The  statement  would  hardly  hold  of  an  oriental 


DISJUNCTIVES   AND   HYPOTHETICALS.  109 

society  in  which  concubinage  was  recognized.  Such  propo- 
sitions, therefore,  express  knowledge,  not  ignorance;  but  it 
is  a  knowledge  of  the  laws  or  general  conditions  of  existence 
prevailing  in  any  sphere  or  '  universe  ',  not  of  the  precise 
state  of  some  particular  individual  in  that  universe. 

In  the  example  just  discussed  the  proposition  affirming 
the  existence  jof -a  general  law  happened  to  be  disjunctive. 
It  is  more  common  to  affirm  such  laws  in  hypothetical,  or 
even  in  universal  categorical  propositions,  e.g.,  If  a  man  is 
insulted  he  becomes  angry,  or  Insulted  men  become  angry; 
When  it  rains  hard  the  streets  are  wet,  or  Hard  rains  wet 
the  streets;  The  nearer  bodies  get  together  the  more  they 
attract  each  other,  or  Contiguous  bodies  attract  each  other 
more  than  those  that  are  farther  apart.  * 

*  On  p.  87  there  are  examples  taken  from  Keynes  of  several  other 
universal  propositions  of  this  kind.  Such  propositions,  as  we  there  saw, 
do  not  necessarily  imply  the  existence  of  things  as  they  are  described  in 
the  grammatical  subjects  of  the  propositions  ;  but  they  do  imply  the 
existence  of  a  universe  whose  laws  they  more  or  less  accurately  express. 
There  doubtless  are  universal  propositions  founded  upon  direct  observa- 
tion of  the  things  named  in  them  and  intended  to  imply  the  existence  of 
those  things  as  well  as  to  describe  them  ;  e.g.,  None  of  the  Stuarts 
were  good  sovereigns  ;  Each  of  the  United  States  contains  colored  citi- 
zens. Such  propositions  cannot  be  put  into  hypothetical  form.  But 
universals  arrived  at  by  deductive  reasoning,  or  reasoning  from  general 
considerations,  are  probably  always  capable  of  being  put  into  hypo- 
thetical form  and  seldom  or  never  necessarily  imply  the  existence  of  the 
things  described  by  their  subjects,  though  they  probably  do  imply  the 
existence  of  the  things  named  in  the  equivalent  hypothetical  proposi- 
tions, e.g.,  Seniors  arc  wiser ..than  S^pJininrr°c;  ;  Every  husband  has  a 
wife.  Turned  into  hypothetical  form  these  propositions  would  run  :  If 
TT"p~erson  belongs  to  the  Senior  class  he  is  wiser  than  if  he  belonged  only 
to  the  Sophomore  class.  If  a  man  is  married,  he  has  a  wife.  The 
general  consideration  in  the  first  of  these  examples  lies  in  the  supposed 
law  of  the  college  universe,  that  two  more  years  of  college  life  must  add 
something  to  one's  wisdom.  It  is  a  statement  which  will  be  as  valid 
as  it  is  now  as  long  as  colleges  and  human  nature  remain  what  they 
are.  It  is  not  concerned  specially  with  the  present,  the  past,  or  the 
future  existence  of  Seniors  and  Sophomores  and  colleges,  the  present 
term  of  the  verb  to  be,  like  the  phrase  must  be,  being  used  in  a  perfectly 


no   FORMAL  CHARACTERISTICS   OF   PROPOSITIONS. 

timeless  sense.  The  proposition  merely  states  the  effects  supposed  to 
result  from  certain  causal  agencies  whenever  and  wherever  they  may  be 
supposed  to  exist.  The  statement  that  every  husband  has  a  wife  is 
based  upon  a  similar  consideration  of  the  nature  of  things.  We  mean 
by  a  husband  a  man  who  is  married,  and  we  know  perfectly  well  that  as 
the  world  is  constituted  men  can  marry  only  women,  that  is,  wives.  It  is 
this  general  fact  which  the  proposition  expresses;  it  does  not  necessarily 
imply  that  any  one  is  married. 

Particular  propositions,  unlike  unjversals,  are  not  usually  deduced 
from  general  considerations  ;  though  sometimes  they  may  be :  e.g., 
'  Some  Sophomores  must  be  wiser  than  the  average  Senior '.  As  a 
rule,  however,  particular  propositions  are  based  upon  the  direct  obser- 
vation of  individuals  to  which  we  are  forced  to  resort  when  general  con- 
siderations are  inapplicable,  and  they  naturally  imply  the  existence  of  the 
individuals  observed.  The  propositions  Some  Sophomores  are  wiser 
than  some  Seniors,  Some  husbands  are  not  happy,  do  not  lay  down 
general  laws  of  the  universe  or  state  the  effects  that  certain  causes  nec- 
essarily produce.  For  this  reason  they  would  hardly  ever  be  put  into 
disjunctive  form,  for  though  such  a  form  is  possible  in  this  case  it  is 
not  very  clear,  and  has  no  special  value  when  the  implication  of  general 
law  is  omitted  ;  e.g.,  A  student  either  is  not  a  Sophomore  or  is  a  mem- 
ber of  a  group  of  persons  some  of  whom  are  wiser  than  some  Seniors. 
Put  into  hypothetical  form  particular  propositions  have  considerable 
significance,  for  they  serve  to  deny  the  existence  of  the  kind  of  law  that 
universals  of  opposite  quality  assert  ;  e.g.,  If  a  person  is  a  Sophomore  he 
may  be  wiser  than  a  Senior.  This  is  the  hypothetical  form  of  the  par- 
ticular proposition  '  Some  Sophomores  are  wiser  than  some  Seniors '. 
They  both  serve  to  deny  the  universal  law  expressed  in  the  universal 
categorical  proposition,  '  No  Sophomore  is  wiser  than  a  Senior ',  or  in 
the  hypothetical  proposition,  '  If  a  student  is  a  Sophomore  he  is  not  as 
wise  as  a  Senior  '. 

Universal  laws  expressible  in  the  above  forms  can  also  be  expressed 
by  the  phrases  must  be,  are  necessarily,  etc.,  and  denied  by  the  phrases 
need  not  be,  are  not  necessarily,  etc. 


CHAPTER    IX. 
THE  OPPOSITION  OF   PROPOSITIONS. 

IN  the  last  two  chapters  we  dealt  with  the  deeper 
pretation  of  propositions.  We  must  now  discuss  another 
question  which  is  practically  one  of  interpretation,  but 
which  is  not  at  all  deep.  Such  a  discussion  is  important 
enough  to  be  found  in  all  the  text-books  of  logic;  and  yet 
the  only  end  which  it  serves  is  to  force  the  reader  to  think 
about  the  obvious  meaning  of  his  words  and  to  show  him 
how  easy  it  is  to  make  foolish  blunders  whj2n_\ve_rattle_pff 
words  \yithout  thinking. 

The  '  Opposition  of  Propositions ',  as  the  phrase  is  used 
in  logic,  means  merely  the  mutual  implications  of  proposi- 
tions which  differ  in  quantity  or  quality  or  both.  To  be 
'  opposed  '  in  this  sense  it  is  therefore  not  necessary  that 
two  propositions  should  be  inconsistent.  This  use  of  the 
term  opposition  is  not  happy,  but  since  it  is  common  we 
must  understand  it. 

Anybody  who  will  exercise  a  little  patience  ought  to  be 
able  to  work  out  an  answer  to  this  question:  Assuming  the 

truth  or  the  falsity  of  one  of  the  propositions  A,    with  com- 
J  mon  propo- 

E,  I,  and  O,  what  can  we  know  about  the  truth   sitions. 

or  falsity  of  the  others  ?  If  it  is  true  that  all  the  members  of 
the  present  senior  class  are  in  good  health  (proposition  A), 
is  it  true  or  false  that  some  of  them  are  in  good  health 
(proposition  I),  that  none  of  them  are  in  good  health 
(proposition  E),  that  some  of  them  are  not  in  good  health 
(proposition  O)  ? 

For  the  sake  of  helping  the  reader  to  verify  his  reasoning 
I  shall  give  a  table  showing  the  relations  of  the  various  cate- 

iii 


I  12 


THE   OPPOSITION   OF   PROPOSITIONS. 


gorical  propositions.  This  table,  like  any  other  that  may  be 
found  in  a  text-book  of  logic,  ought  to  be  understood,  but 
not  learned  by  heart.  The  only  thing  in  logic  that  ever 
ought  to  be  learned  by  heart  is  a  definition,  for  we  must 
depend  upon  memory  for  a  precise  meaning  of  words,  but 
even  a  definition  ought  not  to  be  learned  in  this  way,  if 
there  is  any  other  way  in  which  a  person  can  remember  and 
restate  its  precise  meaning.  With  a  logical  table  the  case 
is  entirely  different.  It  is  valuable  only  because  clear  think- 
ing is  required  to  construct  it.  It  is  not  worth  remember- 
ing; and  to  commit  it  to  heart  like  a  multiplication  table  is 
a  pure  waste  of  time. 


If 

A  is  true, 

E  is 

false, 

I 

true, 

O 

false. 

" 

E  "     » 

A  " 

false, 

I 

false, 

O 

true. 

«' 

I    "     " 

A  " 

doubtful, 

E 

false, 

O 

doubtful. 

" 

O  "     » 

A  " 

false, 

E 

doubtful, 

I 

doubtful. 

<« 

A  is  false, 

E  is 

doubtful, 

I 

doubtful, 

O 

true. 

" 

E  "     " 

A  " 

doubtful, 

I 

true, 

O 

doubtful. 

" 

I    »     " 

A  » 

false, 

E 

true, 

O 

true. 

lt 

O  "    " 

A  " 

true, 

E 

false, 

I 

true. 

This  table  is  concerned  only  with  the  relations  of  universal 
propositions  and  particulars.  It  tells  us  nothing  about  the 
relation  of  either  universals  or  particulars  to  propositions 
which  tell  something  about  some  designated  individual  or 
class  of  individuals  within  the  larger  group.  If  we  designate 
all  propositions  dealing  with  a  designated  individual  or  class 
within  the  larger  group  by  the  letter  S  we  get  the  followng: 


If  A  is  true, 
"  E  "     " 
"  I    "     " 
"  O  "     " 
"  A  is  false,  S 
"  K"    "      S 


S  affirmative  is  true 
S  "  false 

S  "  doubtful 

S  "  doubtful 

"  doubtful 
' '  doubtful 


and  S  negative  is  false. 


false 
true 


true. 

doubtful. 

doubtful. 

doubtful. 

doubtful. 

true. 

false. 


WITH   COMMON   PROPOSITIONS.  113 

If  S  aft.  is  true,  A  is  doubtful,  E  false,  I  true,  O  doubtful. 
If  S  neg.  is  true,  A  is  false,  E  doubtful,  I  doubtful,  O  true.* 

It  should  be  noticed  that  the  truth  of  a  universal  proposi- 
tion involves  the  truth  of  the  corresponding  singulars  and 
particulars,  and  the  falsity  of  a  singular  or  particular  involves 
the  falsity  of  the  corresponding  universal,  but  not  vice  versa. 

Of  propositions  which  differ  only  in  quality,  if  both  are 
particular  one  must  be  true  and  both  may  be;  if  both  are 
universal  one  must  be  false  and  both  may  be.  Of  the 
propositions  A,  E,  I,  O,  having  the  same  subject  and 
predicate,  it  is  only  when  they  differ  in  both  quantity  and 
quality  (i.e.,  A  and  O,  E  and  I),  that  one  must  necessarily 
be  true  and  the  other  false.  Such  propositions  are  called 
contradictories.  Universal  propositions  of  different  quality 
(i.e.,  A  and  E),  are  called  contraries. 

To  '  contradict '  a  statement  is  to  deny  its  truth.  If  you 
make  any  statement  whatever  (e.g. ,  that  the  moon  is  made 
of  green  cheese,  that  every  Englishman  likes  roast  beef),  and 
if  I  say  '  That  is  not  true',  I  contradict  you,  and  the  impor- 
tant thing  to  notice  is  that  if  either  of  us  is  right  the  other 
is  wrong,  and,  vice  versa,  if  either  of  us  is  wrong  the  other  is 
right.  We  cannot  both  be  right,  and  we  cannot  both  be 
wrong.  To  contradict  a  statement  it  is  not  necessary  to 
say  '  That  is  not  true  '  in  these  exact  words.  Any  statement 
contradicts  another  if  the  two  are  so  related  that  when  either 
of  them  is  true  the  other  must  be  false  and  vice  versa.  In 
formal  logic,  however,  contradictory  propositions  are  sup- 
posed also  to  have  the  same  terms  in  the  subject  and  in  the 
predicate,  thus:  '  The  moon  is  made  of  green  cheese'  and 
'  The  moon  is  not  made  of  green  cheese  ',  '  All  Englishmen 
like  roast  beef '  and  '  Some  Englishmen  do  not  like  roast 
beef '.  In  connection  with  this  last  example  it  must  be 

*  It  is  often  said  that  for  logical  purposes  singular  propositions  can  be 
treated  as  universals.  In  the  present  case  they  must  be  treated  rather  as. 
particulars,  though  not  precisely.  In  actual  expedience  the  matter  pre- 
sents no  difficulties. 


114  THE  OPPOSITION  OF  PROPOSITIONS. 

noticed  that  the  contradictory  of  a  universal  proposition  is 
always  either  a  particular  or  a  singular,  and  that  of  a  par- 
ticular a  universal.  Universal  propositions  of  opposite 
quality  ('  All  Englishmen  like  roast  beef ',  '  No  Englishmen 
like  roast  beef')  cannot  be  contradictories;  for  while  they 
cannot  possibly  both  be  true,  they  may  both  be  false.  Such 
propositions  are  always  '  Contraries  '. 

The  lesson  to  be  learned  from  these  facts  is  that  guarded 
statements  are  often  quite  as  useful  as  sweeping  statements 
and  much  safer.  If  two  opponents  make  guarded  state- 
ments both  may  be  right;  if  they  make  sweeping  statements 
they  cannot  both  be  right,  but  both  may  be  wrong;  and  if 
cither  of  them  makes  a  sweeping  statement,  the  other  need 
not  make  a  statement  equally  sweeping  in  order  to  prove 
him  wrong,  for  a  universal  proposition  can  be  disproved  by 
a  single  exception.  Cautious  statements  may  not  always  be 
very  interesting,  but  they  are  not  likely  to  be  ridiculous. 

The  terms  contrary  and  contradictory  are  the  only  ones 
in  this  connection  which  for  ordinary  purposes  are  worth 
remembering.  There  are  others,  however,  whose  meaning 
is  made  clear  enough  in  the  following  traditional  '  square 
of  opposition  ' : 

.. Contraries 17 


%     &      a 

VN         t 

I        <*^V       | 

<«        ,C°         \       g. 

J- Subcontraries — ^ 

A  and  E  are  each  called  a  subalternans  (active). 
I  and  O  are  each  called  a  subalternate  (passive).* 

*  The  table  which  I  have  given  on  p.  112  (not  the  square)  shows  the 
relations  of  the  various  propositions  wh'^n  it  is  taken  for  granted  that 
objects  of  the  kind  described  in  their  subjects  exist.  We;  never  talk 


WITH    EXCLUSIVES   AND   EXCEPTIVES.  115 

What  the  logical  opposites  of  exclusive  and  exceptive 
propositions  are  depends  upon  their  interpretation.  We 

have  seen  that  when  propositions   in  this  form 

.....  .  .  With  exclu- 

relate  concrete    facts   about    individual    objects  sivesand 

.  .  exceptives. 

they  usually  imply  something  about  the  objects 

specifically  mentioned  as  well  as  about  the  other  members 
of  the  class  in  question,  but  that  when  they  express  some 

about  things  that  we  do  not  assume  for  the  moment  at  least  to  exist  in 
some  universe  or  other.  But  when  a  universal  proposition  is  used  as 
the  equivalent  of  a  hypothetical  to  express  a  general  law,  then  the  thing 
as  it  is  described  in  the  subject  of  the  universal  categorical  proposition  is 
not  what  we  are  really  talking  about  and  the  proposition  does  not  neces- 
sarily imply  its  existence.  This  has  been  already  explained.  (See  p.  87.) 
It  has  also  been  pointed  out  that  particular  propositions  usually  do  imply 
the  existence  of  things  as  they  are  described  in  the  subject.  Particular 
propositions  therefore  imply  something  that  one  kind  of  universal  prop- 
ositions do  not  imply.  In  this  case  therefore  the  truth  of  the  universal 
does  not  necessarily  imply  the  truth  of  the  particular.  By  way  of  exam- 
ple let  us  suppose  that  the  universal  proposition  '  Candidates  arriving 
late  are  fined  '  is  equivalent  to  the  hypothetical  '  If  any  candidate 
arrives  late  he  will  be  fined '.  This  statement  may  be  true  as  stating  a 
rule  of  the  board  whether  any  candidate  happens  to  be  late  or  not.  But 
if  the  particular  proposition  '  Some  candidates,  or  some  of  the  candi- 
dates, arriving  late  are  fined'  means  that  there  are  candidates  arriving 
late  and  some  of  them  are  fined;  then  this  statement  is  not  true  unless 
there  are  candidates  arriving  late.  It  may  thus  be  possible  that  the 
universal  proposition  is  true  when  the  particular  is  false. 

Similarly  if  particular  propositions  imply  the  existence  of  candidates 
arriving  late  and  there  are  not  any,  the  propositions  I  and  O  will  both 
be  false  at  the  same  time,  as  they  cannot  be  when  the  existence  of  the 
objects  named  is  taken  for  granted  throughout. 

Keynes  thinks  that  it  can  be  shown  in  a  similar  way  that  "  the  ordi- 
nary doctrine  of  contrariety  does  not  hold  good  ".  If  universal  propo- 
sitions do  not  imply  the  existence  of  the  kind  of  things  described  in  their 
subjects,  "  All  S  is  P  and  no  S  is  /"are  not  inconsistent  with  one  another, 
but  the  force  of  asserting  both  of  them  is  to  deny  that  there  are  any  S's". 
(p.  195.)  To  take  his  example,  if  there  is  no  such  thing  as  an  honest 
miller  it  is  true  that  an  honest  miller  has  a  golden  thumb,  and  it  is  true 
that  he  has  not. 

I  think  that  here  Dr.  Keynes  is  mistaken.  The  statement  that  an 
honest  miller  has  a  golden  thumb  is  equivalent  to  the  hypothetical:  'If 


Il6  THE   OPPOSITION   OF   PROPOSITIONS. 

general  law  or  condition  it  is  only  the  unspecified  members 
of  the  class  about  which  something  is  necessarily  implied. 
'  Only  the  red  pills  are  to  be  taken  '  means  that  the  red  pills 
are  to  be  taken,  and  the  others  left ;  '  Only  the  good  are 
happy  '  means  that  goodness  is  essential  to  happiness,  so 
that  the  bad  are  never  happy ;  but  it  does  not  mean  that 
every  good  man  is  happy. 

To  take  the  last  case  first;  apart  from  the  implication  of 
a  general  law  which  may  be  contradicted  by  saying  that 
virtue  is  not  at  all  essential  to  happiness,  the  proposition  is 
merely  equivalent  to  the  statement  that  no  bad  people  are 
happy,  or  that  all  happy  people  are  good;  and  the  logical 
opposites  of  these  propositions  are  obvious. 

In  the  other  case  (Only  the  red  pills  are  to  be  taken), 
where  an  exceptive  or  exclusive  proposition  is  equivalent  to 
two  ordinary  propositions  (The  red  are  to  be  taken  and  the 
others  are  not  to  be  taken),  it  would  be  false  if  any  of  the 
following  were  true: 

a  miller  is  honest  his  thumb  turns  into  gold '.  Of  course  this  is  intended 
to  imply  that  honest  millers  are  not  to  be  found,  but  it  also  implies  the 
existence  of  some  occult  causal  relation  between  honesty  in  a  miller  and 
a  golden  thumb,  and  a  person  cannot  deny  the  statement  without  imply- 
ing that  this  conception  of  the  universe  is  fictitious. 

On  the  whole  subject  see  Keynes,   pp.  186-210. 

Since  hypothetical  propositions  and  universals  equivalent  to  them  are 
usually  intended  to  imply  the  existence  of  some  general  law.  they  are 
sufficiently  contradicted  by  any  proposition  denying  the  existence  of  such 
a  law.  The  equivalent  statements  '  If  a  man  is  rich  he  is  stingy  '  and 
'  All  rich  men  are  stingy '  can  be  always  contradicted  by  the  statement 
'  It  is  not  always  so';  but  if  the  supposed  causal  relation  between  riches 
and  stinginess  were  the  real  subject  of  interest  it  would  be  sufficient  to 
say  '  It  is  not  necessarily  so';  and  this  might  be  proved  even  though  no 
concrete  exception  to  the  universal  categorical  proposition  could  be  found. 
To  put  the  matter  otherwise:  Hypothetical  propositions  tell  what  under 
certain  circumstances  must  be.  To  contradict  them  it  is  sufficient  to  say 
that  it  need  not  be.  This  can  be  proved  by  sliowing  that  it  sometimes 
is  not,  but  if  a  concrete  exception  could  not  be  found  it  might  be  proved 
in  some  other  w;iy. 


SYMBOLS.  1 1 7 

(1)  Neither  the  red  are  to  be  taken  nor  the  others  not  to 
be  taken  =  The  others  alone  are  to  be  taken. 

(2)  The  red  or  some  of  the  red  are  not  to  be  taken. 

(3)  The  others  or  some  of  them  are  to  be  taken. 

(4)  Either  the  red  or  some  of  them  are  not  to  be  taken 
or  the  others  or  some  of  them  are  to  be  taken. 

The  last  of  these  four  propositions — the  disjunctive — is 
the  only  one  that  must  necessarily  be  true  when  the  original 
proposition  is  false.  It  therefore  is  its  contradictory.  The 
first  of  the  four  is  the  most  extreme  statement  in  the  other 
direction.  It  therefore  is  the  contrary  of  the  original.  The 
other  two  are  contraries  or  contradictories  of  the  parts  into 
which  the  original  is  resolved. 

From  all  this  it  can  be  seen  that  a  logical  opposite  of  an 
exclusive  or  exceptive  proposition  is  itself  rarely  exclusive 
or  exceptive. 

To  give   concreteness   to  what  has  been  said  about   the 

opposition  of  propositions  the  following  system 

Symbols, 
of  symbols  is  suggested. 

Let  a  small  circle  represent  any  object  S  of  the  kind  dis- 
cussed, and  a  plain  stroke  through  it  (j)  indicate  the  presence 
of  a  given  attribute  P,  while  a  stroke  with  a  small  bar  or 
tick  across  it  (j)  indicates  the  absence  of  that  attribute.  It 
is  evident  that  the  stroke  cannot  be  both  plain  and 
crossed. 

Suppose  all  the  objects  of  the  kind  discussed  to  be  repre- 
sented by  a  number  of  small  circles.  When  anything  is  said 
about  all  the  objects  of  the  kind  under  discussion  draw  a 
plain  or  ticked  stroke  as  the  case  may  be  through  each  of 
the  little  circles.  When  something  is  said  about  only  some 
of  the  objects  leave  some  of  the  circles  unmarked.  The 
result  is  as  follows: 

A:  All  S  is  P  (J>  (J)  cj) 

E:  No  S  is  P  j>  i  i 

I:  Some  S  is  P  (f)  ({)  o 

O :  Some  S  is  not  P  (j)  o  (J) 


nS  THE   OPPOSITION   OF   PROPOSITIONS. 

I  and  O :  Some  S  is  P  and  some  is  not  (j)  (j)  (j)  ^)  O 

To  show  how  these  symbols  help.  Let  us  represent  the 
supposed  fact  that  All  S  is  P — that  every  circle  has  a  plain 
stroke  through  it — thus:  (J)  (j)  (})  (j)  It  does  not  matter 
how  many  of  these  circles  we  draw  so  long  as  the  plain  stroke 
is  drawn  through  each  one  of  them,  to  show  that  there  are 
no  exceptions. 

Now  suppose  the  question  to  arise:  How  many  of  these 
S's  have  a  crossed  stroke  ?  We  need  only  glance  at  the 
circles  to  see  that  there  are  none  marked  that  way  and  no 
unmarked  circles  that  might  be  marked  that  way.  Hence 
we  say:  None  of  the  circles  can  be  marked  with  a  crossed 
stroke;  none  of  the  S's  can  be  non-P;  no  S  is  non-P.  Thus 
the  symbols  enable  us  to  see  that  this  follows  from  the  sup- 
posed fact  that  each  of  the  S's  is  P.  In  the  same  way  if  each 
of  the  S's  is  P — if  each  circle  has  a  plain  stroke — we  need 
only  look  at  the  above  figures  to  sec  that  it  is  also  true  that 
at  least  some  of  the  circles  have  plain  strokes — that  some 
S's  are  P  (Proposition  I);  false  that  some  of  the  circles  have 
not  plain  strokes — -that  some  S's  are  not  P  (Proposition  O) ; 
ami  still  more  false  that  none  of  the  circles  have  plain  strokes 
— that  no  S's  are  P  (Proposition  E). 

Again,  let  us  suppose  that  some  S's  are  not  P  (Proposition 
O)  and  represent  it  by  drawing  a  crossed  stroke  through 
some  but  not  all  of  the  circles — it  does  not  matter  how 
many:  cj)  (j)  o  O  We  leave  some  of  the  circles  unmarked 
because  there  are  some  that  the  proposition  does  not  say 
anything  about.  We  know  that  in  reality  each  of  these 
must  have  one  character  or  the  other,  but  we  do  not  attempt 
to  represent  it  until  we  know  which  character  it  is. 

What  now  can  we  say  about  the  truth  or  falsity  of  the 
statement  that  no  S's  are  P  (Proposition  K) — that  none  of 
the  circles  should  really  be  marked  with  a  plain  stroke? 
All  we  can  say  is  that  the  marks  already  there  will  not  tell 
us.  In  other  words,  if  we  know  that  Proposition  O  is  true 


SYMBOLS.  119 

and  if  that  is  all  we  know,  we  must  remain  in  doubt  about  the 
truth  or  falsity  of  E.  So  likewise  with  I ;  so  long  as  we  do 
not  know  whether  those  unmarked  circles  should  really  be 
marked  with  a  plain  stroke  or  with  a  crossed  stroke  we 
cannot  say  whether  it  is  true  or  false  that  some  S's  are 
not  P.  We  can  tell,  however,  about  the  truth  or  falsity  of 
A ;  for  if  A  were  true  and  all  S's  were  P,  all  the  circles  would 
have  to  be  marked  with  a  plain  stroke,  and  that  is  not  possi- 
ble so  long  as  at  least  some  of  them  are  marked  with  a 
crossed  stroke.  Hence  we  can  see  from  the  symbols  that 
represent  the  truth  of  O  that  A  must  be  false.  And  so  of 
the  rest. 

So  far  no  particular  S  has  been  definitely  and  individually 
designated.  To  indicate  some  particular  individual  or  sub- 
group of  individuals  use  a  small  black  dot  or  blacken  the 
circle.  All  the  remaining  categorical  propositions  can  then 
be  symbolized. 

Singular  A  :  Socrates  is  P  « 

Singular  E:   Plato  is  not  P  e 

Exceptive  A:  All  the  S's  but  B  are  P      CJ)  <j)  <^  or  (j)  (|)  • 
The  first  of  these  figures  indicates  '  All  the  S's  but  B  are 
P  (and  B  is  not)',  the  second  indicates  '  All  the  S's  but  B 
are  P  (and  it  is  not  said  whether  B  is  P  or  not)'. 

Exceptive  E :  No  S  but  BisP         (j)  (j)  ^    or    (j)  (j)  • 
Exclusive  A :   B  is  the  only  S  which  is  P  (j)  ^  cj) 

Exclusive  E:   B  is  the  only  S  which  is  not  P  f  (j)  (j) 

It  is  to  be  noticed  that  a  person  interpreting  these  diagrams 
could  not  distinguish  between  a  proposition  and  its  '  ob- 
verse';  for  example,  between  the  affirmative  proposition  All 
S  is  P  and  the  negative  No  S  is  non-P,  or  between  the  nega- 
tive No  S  is  P  and  the  affirmative  All  S  is  non-P.  This  is  an 
advantage  rather  than  a  defect;  indeed  the  whole  value  of  the 
symbols  rests  upon  such  facts,  for  the  difference  between  a 
proposition  and  its  obverse  expresses  a  difference  of  shading 
or  accent  in  the  thought,  but  not  a  difference  in  the  objects 
thought  about.  The  relations  of  the  objects  remain  the 


120  THE   OPPOSITION   OF   PROPOSITIONS. 

same  whether  they  are  told  about  in  one  way  or  in  another, 
and  the  diagrams  symbolize  these  relations  as  they  are  sup- 
posed to  exist  in  the  objects.  They  point  to  the  reality  with 
which  thought  is  concerned  and  to  which  it  must  always 
conform  whatever  its  shading,  rather  than  to  the  particular 
shading  which  the  thought  may  happen  to  take  or  the  words 
in  which  it  happens  to  be  expressed,  and  they  can  be  used 
to  test  the  thought  no  matter  what  its  shading  or  form  of 
expression. 

The  fact  that  these  diagrams  express  no  difference  between 
a  proposition  and  its  obverse  suggests  the  question  that  is 
sometimes  discussed  whether  proposition  A  is  not  after  all 
negative  rather  than  affirmative.  When  we  say  that  every 
nation  prefers  its  own  interests  to  the  good  of  humanity 
(All  S  is  P),  do  we  have  in  mind  all  the  nations  that  do  this, 
or  the  fact  that  none  can  be  found  which  does  not  ?  Cer- 
tainly we  cannot  be  sure  that  the  statement  is  true  until  we 
find  that  there  is  no  nation  which  does  not  (No  S  is  non-P). 
Perhaps  we  can  say  that  when  proposition  A  expresses  a 
hasty  and  unverified  generalization  it  is  affirmative,  when  it 
is  derived  deductively  from  general  considerations  it  may 
also  be  affirmative,  but  when  it  is  reached  cautiously  in  the 
absence  of  general  considerations  it  is  usually  negative. 
When  we  seek  to  verify  a  general  statement,  we  do  not  count 
the  cases  in  which  it  holds,  but  we  look  for  exceptions.* 

*  This  system  (if  diagrams  seems  to  me  to  indicate  the  opposition  of 
propositions  better  than  Euler's  (explained  elsewhere),  partly  because 
it  provides  a  diagram  for  every  proposition,  while  his  only  provides  for 
the  first  four,  partly  because  the  same  diagram  represents  a  proposition 
and  its  obverse,  partly  because  the  diagrams  for  all  the  propositions  that 
express  different  facts  are  distinctly  different,  but  mainly  because  it  pre- 
serves the  distinction  between  things  and  attributes,  and  represents  the 
presence  or  absence  of  the  latter  in  the  former  rather  than  the  partial  or 
complete  inclusion  or  exclusion  of  one  class  by  another. 


CHAPTER   X. 
INFERENCE   AND   THE   SO-CALLED   LAWS   OF   THOUGHT. 

IN  previous  chapters  we  have  given  examples  of  good  and 
bad  inference;  we  have  said  that  all  inference  involves  judg- 
ments about  real  or  supposed  objects  of  thought  different 
from  the  judgments  themselves;  we  have  said  that  these 
judgments  can  be  expressed  in  propositions,  and  in  the 
chapter  on  the  Opposition  of  Propositions  we  have  had 
practical  examples  of  the  relation  between  the  facts  and  the 
propositions  about  them.  We  must  now  inquire  more  fully 
what  inference  really  is.  In  doing  so  we  turn,  though  never 
altogether,  from  the  question  of  words  and  their  meanings 
and  fix  our  attention  more  fully  upon  things  and  their 
relations. 

We  infer  when  we  suppose  that  because  one  state  of  affairs 
exists  another  exists  also.  The  real  or  supposed  facts  that 

we  reason  from  are  called  premises;  those  that 

Inference— 
we  reason  to,  conclusions  ;  and  we  may  say  that    what. 

the  conclusion  of  any  argument  is  true  because  the  premises 
are  true,  or  that  the  premises  are  true  and  therefore  the 
conclusion  is  true. 

Clear  as  this  matter  seems  it  is  not  fully  understood  until 
we  distinguish  the  relation  of  premise  and  conclusion  from 
two  other  relations  each  of  which  may  likewise  be  indicated 
by  the  words  '  because  '  and  '  therefore  ',  namely,  the  rela- 
tion of  cause  and  effect  and  that  of  motive  and  act.  A 
man  may  say,  for  example,  that  he  believes  in  Christianity 
because  he  was  born  and  bred  in  a  Christian  community,  or 

121 


122       INFERENCE   AND   THE   LAWS   OF   THOUGHT. 

because  he  wants  to  go  to  heaven,  or  because  the  four 
gospels  and  the  sacraments  of  the  Church  must  have  had 
some  cause.  The  first  '  because  '  indicates  a  cause,  the 
second  a  motive,  the  third  a  premise.  The  knowledge  that 
such  and  such  causes  or  motives  exist  may  enable  us  to  infer 
the  existence  of  the  corresponding  effects  or  acts.  If  it  is 
raining  we  know  that  people  will  put  up  their  umbrellas. 
Similarly  the  knowledge  that  the  effects  or  acts  exist  may 
enable  us  to  infer  the  existence  of  the  causes  or  motives. 
If  people  have  up  their  umbrellas  we  know  that  it  is  raining. 
But  with  causes  and  motives  as  such,  inference  has  no 
more  to  do  than  with  any  other  relations. 

Inferences  are  usually  divided  into  two  classes:  Deductive, 
or  those  in  which  conclusions  follow  so  necessarily  from 

their  premises  that  their  truth  is  as  certain  as  that 
Deduction.  .  ,  ,  ,    T     , 

of    the  premises   themselves;   and   Inductive,    or 

those  in  which  the  conclusion  follows  from  the  premises  with 
more  or  less  probability,  but  by  no  means  so  inevitably — so 
that  the  premises  might  sometimes  be  true  and  yet  the  con- 
clusion be  false.  To  illustrate  the  latter  first  :  from  the 
presence  of  dark  clouds  and  a  moist  atmosphere  we  can  infer 
that  it  will  rain,  but  we  cannot  be  certain  of  it.  On  the 
other  hand,  if  we  know  that  on  cloudy  days  it  always  rains 
and  that  to-day  it  is  cloudy,  we  can  be  quite  certain  that 
there  has  been  or  will  be  rain  to-day. 

Deductive  inference  is  the  only  kind  that  logicians  dis- 
cussed for  two  thousand  years.  All  that  we  shall  have  to 
say  in  the  next  seven  chapters  has  direct  reference  to  it. 
Induction  will  be  discussed  afterwards;  something  also  will 
be  said  about  the  relation  between  the  t\vo  kinds  of  infer- 
ence. In  the  meantime  we  need  only  say  that  there  is  not 
nearly  so  much  difference  between  them  as  has  often  been 
supposed. 

Deduction,  or  the  absolutely  indisputable  kind  of  infer- 
ence, does  not  depend,  as  most  logicians  have  assumed, 
upon  any  special  relation  between  our  thoughts,  but — like 


DEDUCTION.  123 

the  other  kind — it  depends  upon  the  nature  and  inner  rela- 
tions of  the  objects  thought  about.  It  can  be  drawn  only 
when  the  stale  of  affairs  asserted  lv  the  premise  or  premises 
could  not  possibly  e.vist  without  the  state  of  affairs  asserted  ly 
the  conclusion,  or  in  other  words,  only  when  what  is  asserted 
by  the  premise  or  premises  and  what  is  asserted  by  the  con- 
clusion are  different  aspects  of  some  wider  system  in  which 
the  former  could  not  exist  without  the  latter.  If  the  line  A 
cuts  the  line  B  we  can  infer  with  absolute  certainty  that  the 
line  B  cuts  the  line  A,  because  one  cannot  cut  the  other 
without  making  some  such  figure  as  this  -J-,  in  which  the 
other  also  cuts  the  one. 

To  take  another  example:  If  anyone  is  told  that  three 
athletic  teams,  A,  B,  and  C,  each  played  three  games  with 
each  of  the  others,  that  there  were  no  drawn  games,  and  that 
A  won  twice  and  twice  only  from  B  and  twice  and  twice  only 
from  C,  while  B  won  only  once  from  C,  he  has  been  told 
enough  to  enable  him  to  construct  a  general  scheme  of 
things  that  includes  also  the  number  of  games  won  by  C  and 
the  relative  standing  of  the  teams:  facts  about  which  he  was 
told  nothing,  and  which  even  now  some  reader  may  not  take 
the  trouble  to  work  out.  That  it  can  be  worked  out  is  not 
due  primarily  to  any  relation  between  the  ideas  merely  as 
ideas  of  the  person  working  it  out;  but  it  is  due  to  the  fact 
which  he  knows,  and  which  would  exist  whether  he  knew  it 
or  not,  that  when  a  contestant  plays  a  game  which  is  not 
drawn  he  must  cither  win  it  or  lose  it,  and  if  he  does  not 
win  it  his  opponent  does,  and  to  the  known  relations  of 
number.  If  the  rules  of  the  game  made  it  possible  for  both 
sides  to  win  or  for  both  to  lose,  or  if  two  from  three  left  two 
instead  of  one,  the  reasoning  to  be  correct  would  have  to 
take  these  facts  into  account  and  the  conclusion  would  be 
different. 

A  curved  surface  cannot  be  concave  on  one  side  without 
being  convex  on  the  other;  and  in  general  the  nature  of 
•things  is  such  that  every  variation  in  one  aspect  of  a  complex 


124       INFERENCE   AND   THE   LAWS   OF   THOUGHT. 

state  of  affairs  involves  a  corresponding  variation  in  some 
other  aspect.  To  infer  we  must  know  what  some  one  aspect 
of  the  situation  really  is  and  the  rule  according  to  which  it 
involves  another  aspect.  Our  knowledge  of  the  first  aspect 
is  the  premise  of  our  reasoning,  and  from  our  knowledge  of 
this  aspect  and  of  the  rule  we  can  reach  the  conclusion,  or 
a  knowledge  of  the  other  aspect.  But  if  various  aspects  of 
a  situation  did  not  involve  each  other  whether  we  reasoned 
about  them  or  not,  we  should  not  be  able  to  reason  at  all. 

It  is  thus  not  the  business  of  logic — or  of  any  part  of  it — 
as  most  writers  have  said  that  it  is,  to  describe  '  necessary 
forms  or  laws  of  thought '  connecting  one  idea  with  another, 
but  rather  to  direct  attention  to  the  most  fundamental  laws 
or  relations  of  things  which  all  reasoning  takes  for  granted 
and  which  alone  make  it  possible  for  any  one  state  of  affairs 
to  involve  any  other. 

If  this  is  a  correct  account  of  the  nature  of  inference  in 
general,  the  only  way  to  test  the  validity  of  any  specific  case 
of  inference  is  to  ask  :  Is  there  any  possible  way  in  which  the 
relations  asserted  in  the  premises  could  exist  in  the  absence 
of  those  asserted  in  the  conclusion  ?  Is  it  possible  for  one 
and  the  same  object  or  general  state  of  affairs  to  have  the 
one  set  of  relations  without  the  other  also  ?  If  it  is  possible, 
then  the  denial  of  the  conclusion  may  be  consistent  with  the 
affirmation  of  the  premises;  if  it  is  not  possible,  this  denial 
is  not  consistent,  and  the  conclusion  folloivs. 

Logical  Consistency  is  thus  a  matter  of  possibility  and 
impossibility  in  the  objects  under  discussion.  This  will 
become  clearer  as  we  proceed. 

Though  the  ultimate  justification  of  every  act  of  inference 
must  be  found  in  the  nature  of  the  things  about  which  the 

inference  is  drawn,  it  would  not  be  possible  for 
The  three  .  , 

•Laws of        us  to  draw  an  inference  unless  we  were  able  to 

think  of  these  things  in  some  coherent  and 
rational  way.  The  fundamental  elements  involved  in  all 
such  coherent  and  rational  thinking  are  known  as  the  '  Three 


THE   THREE    'LAWS    OF   THOUGHT*.  125 

Laws  of  Thought ' ;  and  we  must  now  explain  what  these 
so-called  laws  of  thought  really  mean. 

The  first  of  these  is  called  the  Law  of  Identity;  it  is 
usually  stated  in  some  such  form  as  this:  'What  is,  is', 
'  A  is  A  ',  '  Everything  is  what  it  is  ';  and  this  law  with  the 
two  others  are  treated  as  axioms  or  first  principles  to  which 
doubtful  arguments  should  be  referred,  and  by  which  alone 
they  can  always  be  tested. 

This  first  law  of  thought — the  law  of  identity — does  not 
mean  that  objects  cannot  change  or  cease  to  exist,  that  A 
cannot  become  B  or  be  wiped  out  of  existence  altogether, 
that  what  is  true  at  one  moment  is  always  true.  It  merely 
expresses  the  fact  that  we  know  what  we  are  thinking  about 
and  what  we  are  thinking  about  it;  that  we  can  recognize 
an  old  object  of  thought  as  the  same  even  when  what  we 
think  about  it  is  not  the  same,  and  that  in  a  similar  way  we 
can  recognize  whether  a  new  statement  about  it  is  or  is  not 
the  same  as  an  old  one.  We  can  consider  an  object  or  a 
situation  in  as  many  aspects  as  we  please  and  still  recognize 
that  we  are  concerned  with  the  same  object  or  situation. 
A  person  can  say,  for  example,  that  a  certain  house  is  red, 
that  it  is  four  stories  high,  that  it  is  old,  and  that  it  was  once 
inhabited  by  George  Washington;  and  the  speaker  and  his 
hearers  can  both  recognize  that  he  is  talking  about  the  same 
house  all  the  time.  But  if  he  should  add  something  about 
its  pale-green  color,  its  snowy  peaks,  its  delicious  flavor,  its 
angry  billows,  its  flushed  and  anxious  countenance  and  its 
relation  to  the  square  root  of  the  difference,  we  should  then 
say  that  his  mind  was  wandering,  his  thought  was  not  con- 
secutive, his  various  '  i/s '  did  not  refer  to  the  same  object. 
We,  the  hearers,  could  say  that  the  objects  referred  to  must 
all  be  different,  but  if  the  speaker's  mind  were  really  wander- 
ing, if  he  were  utterly  incapable  of  holding  fast  to  an  old 
object  of  thought  and  identifying  it,  he  would  not  know 
that  his  various  sentences  referred  to  different  objects,  for 
without  the  power  to  identify  an  old  object  of  thought  he 


126       INFERENCE   AND   THE   LAWS   OF   THOUGHT. 

would  have  no  more  idea  of  difference  than  of  identity.  To 
him  no  pronoun  could  have  an  antecedent  and  the  words 
'  same  '  and  '  different '  would  be  absolutely  meaningless. 

This  illustration  has  particular  reference  to  the  object 
thought  about,  but  the  power  of  remembering  and  recogniz- 
ing statements  made  about  it  is  just  as  essential  to  sanity. 
The  law  of  identity  thus  expresses  the  fact  that  thought 
points  to  objects  and  that  we  can  know  or  recognize  what 
objects  we  are  thinking  about  and  what  we  are  thinking 
about  them. 

The  second  '  law  of  thought  '  is  called  the  Law  of  Contra- 
diction, and  is  expressed  in  such  formulas  as  these  :  '  Nothing 
can  both  be  and  not  be  ',  '  A  is  not  not- A  ',  'A  cannot  be  both 
B  and  not-B  '.  While  the  law  of  identity  rests  upon  our  power 
of  identifying  an  object  of  thought,  the  law  of  contradiction 
rests  upon  our  power  of  distinguishing  between  an  affirmation 
and  a  denial,  between  the  meaning  of  'is'  and  the  meaning 
of  '  is  not ',  of  'yes  '  and  of  '  no  '.  The  law,  in  its  primary 
sense,  at  least,  simply  means, — what  everybody  knows, — 
that  we  cannot  both  affirm  and  deny  the  same  thing  about  the 
same  object.  Understanding  by  S  whatever  can  be  named 
in  the  subject  of  a  sentence,  and  by  P  whatever  can  be  named 
in  the  predicate,  the  law  means:-  If  it  is  true  that  S  is  P,  then 
it  is  false  that  S  is  not  P  and  if  it  is  true  that  S  is  not  P, 
then  it  is  false  that  S  is  P.  The  law  as  thus  stated  does  not 
depend  upon  any  particular  knowledge  about  things  ;  it  fol- 
lows inevitably  from  the  nature  of  thought.  Why  thought 
should  take  the  form  of  a  judgment,  and  why  affirmative  and 
negative  judgments  should  exclude  each  other  we  do  not 
know,  but  as  soon  as  we  know  anything  about  ourselves  we 
know  that  such  is  the  case. 

There  is  a  secondary  meaning  often  attached  to  the  law  of 
contradiction,  namely  :  that  we  must  not  ascribe  incompat- 
ible qualities  or  relations  to  the  same  object.  According  to 
the  primary  sense  of  the  law  we  contradict  ourselves  if  we  say 
that  a  certain  thing  is  white  and  that  it  isn't  white;  accord- 


THE   THREE    'LAWS   OK   THOUGHT'.  127 

ing  to  the  secondary  sense  \ve  contradict  ourselves  if  \ve  say 
it  is  white  and  that  it  is  black.  In  the  first  case  we  had  in 
mind  the  same  quality — white,  and  the  law  said  we  could  not 
both  affirm  and  deny  it ;  in  the  second  rase  we  had  in  mind 
two  different  qualities,  and  the  law  said  we  could  not  affirm 
them  both.  In  the  first  case  the  sense  of  contradiction  is  due 
to  the  fact  that  it  is  mentally  impossible  to  affirm  and  to  deny 
the  same  thing  at  the  same  time,  just  as  it  is  physically  im- 
possible to  say  yes  and  no  at  the  same  time,  to  nod  the  head 
and  to  shake  it,  to  approach  or  draw  a  thing  toward  you  and 
to  recede  or  push  it  away;  in  the  second  case  it  rests  upon 
our  knowledge  that  the  same  object  cannot  have  two  different 
colors  at  once.  In  the  first  case  the  contradiction  rests  upon 
the  nature  of  a  judgment  and  could  be  recognized  by  any  one 
who  could  distinguish  between  the  meanings  of  '  is '  ami 
'is  not',  however  limited  his  experience;  in  the  second 
case  it  rests  upon  the  nature  of  things  as  people  gifted  with 
sight  believe  them  to  be. 

If  we  did  not  believe  in  the  existence  of  a  world  so  con- 
stituted that  the  presence  of  any  quality  in  a  thing  excludes 
certain  other  qualities,  we  should  not  recognize  any  con- 
tradiction in  saying  that  a  thing  is  both  white  and  black, 
three  feet  long  and  one  inch  long,  round  and  square,  before 
and  after. 

The  qualities  which  do  not,  or  cannot,  exist  together 
in  the  same  thing  happen  to  be  those  which  appeal  to 
the  same  sense,  and  which  we  are  therefore  able  to  com- 
pare together,  and  for  which  we  usually  have  some  general 
name,  such  as  'color',  'size',  'shape',  'time',  'place'. 
Incomparable  qualities,  such  as  red  and  square,  may  or  may 
not  coexist  in  the  same  object,  and  we  have  no  difficulty 
in  imagining  any  combination  of  them.  Either  because  of 

O  O  . 

the  nature  of  our  faculties  or  because  of  the  limitations  of 

our  experience,  we  cannot  imagine  an   object  which  has  at 

the  same  time  two  different  qualities  of  the  same  general  kind. 

Because  we  cannot  imagine  a  thing  to  have  at  once  two 


128       INFERENCE   AND   THE   LAWS   OF   THOUGHT. 

qualities  of  the  same  general  kind,  we  assume  that  such  quali- 
ties cannot  really  coexist,  and  when  we  assume  this,  it  follows 
that  to  affirm  one  quality  of  an  object  is  equivalent  to  deny- 
ing another,  so  that  when  any  one  says  that  a  thing  is  large 
and  small,  white  and  black,  we  take  it  for  granted  he  means 
that  it  is  large  and  isn't  large,  that  it  is  white  and  isn't  white, 
and  that  he  is  therefore  contradicting  himself.  Thus  through 
the  limitations  of  our  imagination  the  law  of  contradiction, 
which  in  its  primary  sense  is  concerned  only  with  the  imposi- 
bility  of  both  affirming  and  denying  the  same  qualities  or  re- 
lations, comes  to  take  on  a  secondary  meaning  concerned 
with  the  inconsistency  of  affirming  certain  different  qualities 
or  relations.*  It  is  this  secondary  sense  of  the  law  that  is 
expressed  in  the  last  two  formulae  I  gave  for  its  expression. 

The  third  general  principle  or  law  of  thought  is  called  the 
Law  of  Excluded  Middle.  The  usual  formula  is  '  Everything 
must  either  be  or  not  be  ',  'A  must  be  either  B  or  not  13  '. 
This  law  is  the  complement  of  the  Law  of  Contradiction  and 
means  that  every  statement  must  be  either  true  or  false.  If  it 
is  false  that  S  is  P,  then  it  is  true  that  S  is  not  P,  and  if  it  is 
false  that  S  is  not  P,  then  it  is  true  that  S  is  P.  This  law, 
like  the  law  of  contradiction  in  its  primary  and  proper  sense, 
is  not  derived  from  an  examination  of  things,  but  follows  in- 
evitably from  the  nature  of  thought  in  judging  ;  for  not  only 
do  affirmative  and  negative  judgments  necessarily  exclude 
each  other,  as  the  law  of  contradiction  says,  but  every  pos- 
itive or  active  judgment  must  either  affirm  something  or  deny 
it  ;  there  is  no  middle  ground. 

Like  the  law  of  contradiction,  the  law  of  excluded  middle 
has  also  acquired  a  secondary  meaning,  concerned  not  with  the 
difference  between  affirmation  and  negation,  but  with  the 
mutual  implications  of  various  qualities  and  relations  in  the 
objects  judged  about. 

*  If  we  distinguish  Ix-tween  the  copula  and  the  predicate  we  can  say 
that  in  its  primary  sense  the  law  is  a  mere  matter  of  the  copula;  but  in 
its  secondary  sense  is  made  a  matter  of  the  predicate. 


THE   THREE    'LAWS   OF   THOUGHT'.  129 

Experience  teaches  that  every  real  thing,  indeed  every 
object  of  which  it  is  possible  to  think  at  all,  has  qualities  and 
relations  of  some  kind.  If  it  is  not  large  it  is  small,  if  it  is 
not  here  it  is  elsewhere  ;  or  else  it  is  a  spirit  or  some  other 
kind  of  immaterial  object  existing  without  space-relations, 
but  not  without  the  moral  or  other  relations  which  that  kind 
of  immaterial  objects  possess.  In  general,  if  any  object,  S, 
has  not  a  certain  quality  or  relation,  P,  it  must  have  some 
other  quality  or  relation  incompatible  with  P,  and  which  we 
may  therefore  call  not-P  or  non-P.  To  put  it  more  briefly  : 
If  S  isn't  P  it  is  non-P;  every  S  must  be  either  P  or  non-P  ; 
and  to  say  that  S  isn't  P  is  equivalent  to  saying  that  it  is 
non-P. 

This  is  the  secondary  sense  of  the  law  ;  and  it  does  not 
depend,  like  the  primary,  wholly  upon  the  mere  nature  of 
judgment,  but  partly  also  upon  the  fact  that  we  have  never 
found  and  cannot  think  of  an  object  that  does  not  possess 
some  definite  relation  or  other. 

But  there  is  often  still  a  third  implication  which  the  law 
seems  to  cover. 

From  earliest  childhood  we  find  those  about  us  dividing 
objects  into  various  kinds,  and  in  the  course  of  experience  we 
learn  to  take  it  for  granted  that  however  much  they  may 
differ  from  each  other  all  objects  of  the  same  kind  are  deter- 
mined in  the  same  respects  ;  have  the  same  kind  of  qualities 
and  relations.  Every  man  has  some  moral  standing.  Hence 
if  he  is  not  good  he  must  be  bad.  He  has  some  color. 
Hence  if  he  is  not  white  he  must  be  black,  brown,  yellow, 
or  red.  And  so  of  size,  weight,  and  all  the  other  general 
qualities  which  every  man  possesses. 

Now,  as  it  happens,  it  is  just  as  easy  to  find  out  that  some 
object,  say  the  soul  or  the  square  root  of  33,  has  no  color  or 
weight  or  shape  at  all  as  to  find  out  that  it  js  not  red  or  heavy 
or  round,  and  in  ninety-nine  cases  out  of  a  hundred  it  is  a 
great  deal  more  serviceable  to  say  so.  Consequently  when 
any  one  says  that  some  object,  X,  is  not  red  his  hearer  takes 


130       INFERENCE   AND   THE   LAWS   OF   THOUGHT. 

it  for  granted  that  he  is  talking  about  an  object  that  has  some 
color  or  other,  since  otherwise  he  would  have  said  it  was 
colorless.*  And  so  of  every  other  quality  and.  relation  :  we 
interpret  the  statement  'S  isn't  P'  to  mean  that  S  has  some 
quality  P'  or  P",  which,  though  different  from  P,  belongs 
to  the  same  general  class. 

The  third  matter  which  the  law  of  excluded  middle  seems 
to  cover  is  thus  a  rule  for  the  interpretation  of  language. 
B;it  such  a  rule  is  by  no  means  infallible.  It  is  quite  possible 
to  say  that  a  triangle  is  not  virtuous  without  the  slightest 
intention  of  implying  that  it  is  vicious. 

Assuming  the  truth  of  the  law  in  the  secondary  sense,  and 
understanding  that  the  phrase  non-P  is  used  to  indicate  some 

quality  or  relation  incompatible  with  P,  we  can 
Ob  version.  .  ... 

turn  every  affirmative  proposition  into  an  equiva- 
lent negative,  and  vice  versa  :  '  All  S  is  P  '  (A)  into  '  No 
S  is  non-P'  (E)  ;  'Some  S  isn't  P'  (O)  into  'Some  S  is 
non-P'  (1);  'All  men  are  mortal'  into  'No  men  are  im- 
mortal ';  and  vice  versa. 

The  manipulation  of  propositions  in  this  way  is  called  Ob- 
vcrxi/iti  or  Immediate  Inference  Ly  Piivitive  Conception.  It  is 
less  commonly  known  as  Permutation-  or  Infiniiaiion.  If  we 
wish  a  formal  definition  we  can  say  : 

To  OBVFRT  a  proposition  is  to  deny  or  affirm  the  absence 
or  pix-sence  of  a  relation  whose  presence  or  absence  the  orig- 
inal proposition  affirmed  or  denied. 

*  "Nn  one  would  be  so  fooli>h  as  to  deny  what  no  one  could  have  the 
slightest  temptation  to  attirm.  It  I  say,  then,  that  X  is  not  V,  I  imply 
that  there  an-  certain  dements  in  X,  by  which,  it  they  were  taken  alone, 
it  miidit  be  confounded  with  V.  O4  course  the  elements  of  resemblance 
mav  be  compar.itively  few,  but  something  in  this  case  must  have  oc- 
curred to  briir^'  it  into  prominence."  C.  C.  Everett,  "  Fichte's  Science 
ol  Knowledge  ",  p.  103. 


CHAPTER   XI. 

IMMEDIATE   INFERENCE,  OR   INFERENCE   FROM  A  SINGLE 
PREMISE. 

WHEN  an  inference  is  drawn  from  a  single  premise  it  is 
called  immediate,  when  from  several  premises  taken  together, 
mediate.  The  terms  immediate  and  mediate  as  thus  used 
have  only  a  secondary  reference  to  time.  Their  main 
object  is  to  indicate  the  absence  or  presence  of  some  inter- 
mediate process.  Where  an  inference  rests  upon  several 
premises  and  cannot  be  drawn  from  one  of  them  alone,  the 
intermediate  process  consists  in  constructing  a  notion  of  a 
total  state  of  affairs  according  to  specifications  part  of  which 
are  laid  down  by  one  premise  and  part  by  another.  It  is 
this  total  state  of  affairs  in  which  alone  both  or  all  the  pre- 
mises can  be  realized  that  implicates  the  conclusion.  A 
state  of  affairs  in  which  none  or  only  a  part  of  the  premises 
were  realized  might  implicate  it,  but  we  know  that  this  other 
must. 

We  are  at  present  concerned  with  immediate  inference, 
or  the  cases  in  which  the  state  of  affairs  described  by  a  single 
premise  necessarily  implicates  that  described  in  the  con- 
clusion. 

The  most  interesting  and  important  kind  of  immediate 
inference  is  called  'Conversion'.  In  discussing  obversion 

we  saw   how  it  was   possible    to   pass   from  "one 

,  .  .       Conversion, 

statement  to  another  about  the  same  object  ;   in 

conversion   we    feel  warranted    in   passing  from  a   statement 


132  IMMEDIATE   INFERENCE. 

about  one  object  or  kind  of  object  to  a  statement  about  an- 
other object  or  kind  of  object  about  which  something  has 
been  implied,  though  not  directly  said  in  the  statement 
about  the  first  object.  If,  for  example,  we  should  happen  to 
know  that  some  white  things  are  square  we  should  be  able 
to  infer  that  some  square  things  are  white.  To  be  white  and 
to  be  square  are  two  very  different  matters  ;  but  yet  the 
world  and  our  minds  are  so  constituted  that  a  statement 
about  the  one  class  of  objects  may  serve  as  the  basis  for  a 
statement  about  the  other.*  In  like  manner,  if  a  person 
interested  in  the  city  of  Cleveland  should  be  told  that  it  is 
183  miles  west  of  Buffalo  and  he  should  afterwards  have 
occasion  to  tell  all  that  he  knew  about  Buffalo,  he  would  be 
able  to  say  that  it  is  183  miles  east  of  Cleveland.  If  he  were 
interested  in  places  183  miles  west  of  Buffalo  he  would  be 
able  to  say  that  at  least  one  of  them  was  Cleveland.  And  if 
he  were  interested  in  the  distance  of  183  miles  he  could  say 
that  it  is  as  far  as  from  Buffalo  to  Cleveland. — The  first 
statement  was  about  Cleveland  ;  but  the  fact  asserted  was  of 
such  a  nature  that  it  could  not  be  true  unless  the  other  state- 
ments, not  about  Cleveland  but  about  Buffalo  and  places  183 
miles  west  of  Buffalo  and  the  distance  of  183  miles,  were 
also  true. 

The  doctrine  of  conversion   found  in  most   text-books  on 

logic   provides  for  only  one  of  the  three  inferences  which  is 

here  drawn,  namely:   a   place  183    miles  west  of 

traditional      Buffalo   is  Cleveland.      The  reason  for  this  lies  in 
treatment.         ,  ....  ...... 

the  traditional  way  of  dividing  every  proposition 

into  subject,  predicate,  and  copula,  and  of  regarding  the 
copula  as  a  perfectly  colorless  sign  of  affirmative  or  negative 
predication.  Every  proposition  was  regarded  as  a  kind  of 

*  The  constitution  of  the  world  involved  in  this  particular  case  is  the 
fact  th.it  several  attributes  (e.g.,  whiteness  and  squareness)  may  be 
possessed  with  equal  intimacy  by  the  same  object  ;  in  the  case  about  to  be 
mentioned  it  is  the  fact  that  relations  are  reciprocal — facts  of  so  familiar 
a  kind  that  we  forget  the  debt  our  logic  owes  them. 


THE   TRADITIONAL   TREATMENT.  133 

equation  of  which  the  copula  supplied  only  the  idea  of 
equality  or  non-equality.  Our  original  proposition,  divided 
in  this  way,  would  read 

Subject.      Copula.        Predicate. 

Cleveland  is  (a  place)  183  miles  west  of  Buffalo, 
and  it  would  be  regarded  as  meaning  nothing  more  than  that 
Cleveland  was  identical  with  a-place-i83-miles-west-of-Buf- 
falo.  Regarded  in  this  way  the  proposition  says  nothing 
whatever  about  Buffalo  or  about  183  miles,  but  only  about 
Cleveland  and  a  place  183  miles  west  of  Buffalo.  These  are 
the  terms,  and  they  cannot  be  broken  up,  consequently  the 
only  inference  to  be  drawn,  if  inference  it  is,  except  by 
obversion  or  by  way  of  opposition  is  found  by  reversing  the 
equation,  and  saying  a  place  183  miles  west  of  Buffalo  is 
Cleveland. 

According  to  the  same  way  of  regarding  things  the  propo- 
sition 'John  is  riding  a  horse'  can  be  converted  into  'a 
person  riding  a  horse  is  John',  but  the  traditional  rules  of 
V)gic  make  no  provision  for  any  inference  about  the  horse.* 

*  This  limited  view  of  the  meaning  of  propositions  can  be  easily  ex- 
plained. In  an  age  like  that  of  Plato  and  Aristotle  when  scientific  knowl- 
edge was  thought  to  consist  merely  in  description  and  classification,  it  was 
natural  enough  to  overlook  all  the  relations  asserted  in  propositions  except 
those  of  substance  and  attribute  and  individual  identity,  for  the  causal 
and  other  outer  relations  between  things  had  no  scientific  significance 
except  as  indicating  qualities  of  the  things,  by  which  they  could  be  iden- 
tified and  classified.  From  this  point  of  view  the  statement  that  John  is  rid. 
ing  a  horse  is  of  value  only  as  it  tells  one  of  John's  accidents  or  occasional 
states  by  which  he  might  perhaps  be  identified  or  distinguished  from 
other  people  who  never  ride  or  at  least  did  not  ride  at  the  time  referred 
to.  From  the  same  point  of  view  the  converse  statement  that  a  horse  is 
being  ridden  by  John  has  scientific  significance  only  as  indicating  that 
horses,  or  at  least  this  particular  horse,  can  be  described  as  capable  of 
being  ridden  or  as  having  been  ridden.  This  standpoint  lent  itself  only 
too  easily  to  the  purely  mechanical  and  verbal  treatment  of  propositions 
which  is  still  common.  Certainly  with  modern  writers  this  purely  verbal 
treatment  of  logical  processes  is  only  a  pedagogic  device.  Yet  it  seems 
to  me  that  it  limits  the  usefulness  of  logic  and  that  the  subject  is  capable 
of  being  treated  more  directly. 


134  IMMEDIATE   INFERENCE. 

If  one  were  interested  in  describing  John  the  facts  would 
naturally  be  stated  in  one  way;  if  he  were  interested  in  de- 
scribing the  horse  they  would  be  stated  in  the  other  way. 
But  the  mode  of  statement  was  settled  before  the  logical 
process  began.  It  was  with  the  description  and  classification 
of  things,  not  with  their  outer  relations,  that  logic  was  con- 
cerned. It  therefore  never  occurred  to  the  early  logicians 
that  it  was  a  part  of  their  business  to  show  how  the  state  or 
relations  of  one  thing  at  any  particular  time  involved  corre- 
sponding  conditions  in  something  else.  Except  as  they  con- 
tained data  for  classification  the  mere  spatial  and  temporal 
and  causal  relations  of  things  had  no  logical  import  and 
were  not  worth  analyzing.  It  was  with  descriptions  of 
things,  not  with  events,  that  the  logical  process  began. 

Let  us  assume  for  a  time,  with  the  old  logicians,  that  our 
only  logical  interest  lie.s  in  the  description  and  classification 
of  things,  and  that  every  proposition  with  which  logic  deals 
must  contain  a  subject,  a  predicate,  and  a  copula  whose  sole 
function  is  to  affirm  or  deny  an  equality  or  identity  between 
the  subject  and  predicate.  If  a  proposition  has  not  such  a 
form  it  must  be  given  one  before  it  is  dealt  with  logically, 
so  that  instead  of  saying  '  John  runs  ',  and  '  Ducks  like 
water  ',  we  must  say  '  John  is  running  ',  or  more  properly 
'  John  is  a  creature  who  is  running ',  and  '  Ducks  are 
creatures  who  like  water  '. 

The  frst  thing  to  be  noticed  from  this  standpoint  is  that 
description  merges  insensibly  into  classification.  When  we 
sav  that  ducks  like  water  we  undoubtedly  describe  one  of 
their  characteristics;  but  when  we  say  that  they  are  '  creatures 
who  like  water'  we  may  be  regarded  as  classing  them  with 
other  creatures  who  like  it  (if  such  exist)  as  distinguished 
from  those  who  do  not.  Thus  the  many  relations  really 
expressed  in  propositions  are  reduced  for  logical  purposes  to 
one:  when  the  traditional  logician  says  that  any  object  or 
class  of  objects,  S,  is  P,  all  he  means  is  that  the  object  or 
class  S  is  contained  in  the  class  P. 


THE   TRADITIONAL   TREATMENT.  135 

What  does  this  statement  about  S  enable  us  to  say  about 
the  class  P? — This  is  the  question  of  conversion.  "A 
proposition  is  said  to  be  converted  when  its  terms  are  trans- 
posed, so  that  the  subject  becomes  the  predicate  and  the 
predicate  the  subject"  (Fowler,  p.  80).  Converting  the 
proposition  '  S  is  P  '  in  this  way  we  get  '  P  is  S  '.  But  how 
many  of  the  P's  are  S  ?  From  the  fact  that  all  ducks  like 
water  it  does  not  necessarily  follow  that  every  creature  that 
likes  water  is  a  duck. 

Sir,  I  admit  your  general  rule, 
That  every  poet  is  a  fool ; 
But  you  yourself  will  serve  to  show  it 
That  every  fool  is  not  a  poet. 

The  mediaeval  logician  sought  mechanical  rules  for 
manipulating  words,  and  so  he  asked  '  Is  there  any  rule  by 
which  \ve  can  tell  the  quantity  and  quality  of  propositions 
that  have  been  converted  ?  ',  and  he  found  two  which  could 
always  be  followed  with  safety: 

"  i.  The  quality  of  the  proposition  (affirmative  or  nega- 
tive) must  be  preserved,  and 

"  2.  No  term  must  be  distributed  in  the  Converse,  unless 
it  was  distributed  in  the  Convertend  "  (Jevons,  p.  82). 

The  convertend  means,  of  course,  the  proposition  that  is 
to  be  converted;  and  the  converse  that  obtained  by  convert- 
ing it.  A  term  is  said  to  be  distributed  when  used  in  such  a 
way  as  to  necessarily  include  all  and  not  merely  some  of  the 
members  of  the  class  it  denotes.  The  subjects  of  the 
propositions  A  and  E  are  thus  said  to  be  distributed;  the 
subjects  of  I  and  O  to  be  undistributed.  But  how  about 
the  predicates  ? 

When  anybody  who  has  not  studied  logic  says  that  ducks 
like  water,  he  uses  the  term  '  ducks  '  demonstratively,  and 
he  can  tell  fairly  well  whether  he  means  to  speak  of  all,  or 
of  only  some  or  most,  of  the  creatures  that  the  name  denotes. 
The  other  two  words  in  the  sentence — '  like  water  ' — he  uses 
descriptively  to  tell  something  about  the  ducks.  If  he  is 


136  IMMEDIATE   INFERENCE. 

now  told  that  he  was  really  talking  not  only  about  ducks 
but  also  about  a  class  of  'creatures  that  like  water',  and 
is  asked  whether  he  refers  to  all  or  only  some  of  this  class 
of  creatures,  he  cannot  help  being  puzzled,  for  the  thought 
of  such  a  class  probably  never  entered  his  mind.  That  is 
the  objection  to  what  Sir  William  Hamilton  and  others  have 
called  the  Quantification  of  the  Predicate.  But  if  he  is  com- 
pelled to  answer,  the  only  safe  thing  to  say  is  that  he  means 
that  ducks  are  at  least  some  of  the  creatures  that  like  water. 
Then  his  statement  about  the  ducks  will  be  true  whether 
other  things,  such  as  gulls  and  frogs  and  fishes,  happen  to 
like  water  or  not.  To  put  the  matter  generally:  Affirmative 
propositions,  whether  universal  or  particular,  do  not  distribute 
their  predicates. 

To  convert  an  affirmative  proposition  we  must  therefore 
reverse  the  subject  and  predicate,  retain  the  affirmative 
copula  (rule  i),  and  see  that  the  subject  is  undistributed, 
i.e. ,  that  the  proposition  is  particular  (rule  2).  In  other 
words,  the  converse  of  A  or  I  is  always  I. 

When  a  universal  proposition  is  converted  into  a  universal 
or  a  particular  into  a  particular  it  is  said  to  be  converted 
simply;  but  when  a  universal  is  converted  into  a  particular 
it  is  said  to  be  converted  per  accidens  or  by  limitation.  It 
will  be  noticed  that  when  A  is  converted  into  I  it  cannot  be 
converted  back  again  into  A,  but  only  into  I.  From  the 
fact  that  'all  Rhode  Islanders  are  Americans',  it  follows 
that  '  Some  Americans  are  Rhode  Islanders';  but  all  that 
can  be  inferred  from  the  latter  proposition  is  that  '  Some 
Rhode  Islanders  are  Americans  '. 

In  contrast  with  affirmatives,  negative  propositions  always 
distribute  their  predicates.  The  statement  that  no  cats  like 
water  means  that  cats  and  creatures  that  like  water  form  two 
wholly  distinct  classes,  and  that  no  individual  belongs  to 
them  both.  We  can  therefore  be  as  sure  that  no  single 
creature  that  likes  water  is  a  cat  as  that  no  single  cat  is  a 
creature  that  likes  water.  Thus  the  converse  of  E  (e.g.,  No 


THE   TRADITIONAL   TREATMENT.  137 

cats  like  water)  is  always  E  (No  creatures  that  like  water  are 
cats). 

The  other  negative  proposition,  O,  is  harder  to  deal  with. 
"  In  attempting  to  convert  the  proposition  O  we  encounter 
a  peculiar  difficulty,  because  its  subject  is  undistributed; 
and  yet  the  subject  should  become  by  conversion  the  predi- 
cate of  a  negative  proposition,  which  distributes  its  predi- 
cate "  (Jevons,  p.  83).  If  certain  boys,  A,  B,  and  C,  do 
not  like  water  we  can  be  quite  sure  that  no  creature  that  likes 
water  is  one  of  these  boys  A,  B,  and  C.  Here  it  is  easy 
enough  to  convert;  but  the  statement  that  A,  B,  and  C  do 
not  like  water  is  equivalent  to  three  singular  propositions, 
not  to  a  particular.  If  it  had  been  forgotten  who  these  boys 
were,  one  might  still  be  sure  that  some  boys  do  not  like 
water  (proposition  O);  but  all  that  could  be  said  on  the 
strength  of  this  about  creatures  that  like  water  is  that  none 
of  them  are  some  boys  or  other.  We  could  not  say  that 
none  of  them  are  boys.  We  might  say,  to  be  sure,  that 
some  of  them  are  not  boys,  but  this  would  be  on  the  strength 
of  what  we  know  about  cats  and  monkeys,  not  on  the 
strength  of  the  statement  that  some  boys  do  not  like  water. 
Since  the  statement  that  no  P  is  some  S  or  other  conveys 
practically  no  information  whatever  about  P,  we  must  con- 
clude that  the  proposition  O  cannot  be  con-verted:  nothing 
definite  can  be  said  about  either  some  or  all  of  the  objects 
denotable  *  by  its  predicate. 

Many  logicians  say  in  substance  that  though  O  cannot  be 
converted  in  the  usual  way  we  can  "  apply  a  new  process, 
which  may  be  called  conversion  by  negation,  and  which  con- 
sists in  first  changing  the  convertend  into  an  affirmative 
proposition,  and  then  converting  it  simply  "  (Jevons,  p.  83). 
In  this  way  '  Some  boys  do  not  like  water '  becomes 
'  Some  boys  dislike  water ',  and  converting  this  we  get 

*  I  say  denotable  rather  than  denoted,  because  the  predicate  of  a 
proposition  is  usually  used  to  describe  the  things  pointed  out  by  the  sub- 
ject, not  to  point  out  new  ones. 


138  IMMEDIATE   INFERENCE. 

'  Some  creatures  that  dislike  water  are  boys '.  (Some  S 
isn't  P  =  Some  S  is  non-P  =  Some  non-P  is  S.) 

This  so-called  conversion  ly  negation  consists  simply  in 
converting  the  obverse;  and  it  is  a  process  which  can  be 
applied  just  as  well  to  A  and  E  (though  not  to  I,  whose 
obverse  is  O  and  inconvertible)  as  to  O. 

The  process  of  alternate  obversion  and  conversion  can 
be  carried  through  various  stages  as  follows;  but  it  is  valid 
only  if  the  existence  of  all  the  objects  named  is  presupposed: 

PROPOSITION  A. 

Beginning  with  Obversion.  Beginning  with  Conversion. 

A.   All  S  is  P  =  A.   All  S^is  P  = 

E.   Xo  S  is  non-P  =  I.   Some  P  is  S  = 

E.    Xo  non-P  is  S  —  O.   Some  P  isn't  non-S. 

A.   All  non-P  is  non-S  = 
1.    Some  non-S  is  non-P  — 

j  Some  non-S  isn't  non-non-P,  or 

{  Some  non  S  isn't  P. 

PROPOSITION   E. 

Beginning  with  Obversion.  Beginning  with  Conversion.  ' 

E.   Xo  S  is  P.  E.    No  S  is  P  = 

A.    All  S  is  non-P.  E.    Xo  P  is  S  = 

I.    Some  non-P  is  S.  A.    All  P  is  non-S  = 

O.    Some  non-P  isn't  non-S.      I.    Some  non-S  is  P  = 

O.  Some  non-S  isn't  non-P. 
PROPOSITION  I. 

Beginning  with  Obversion.  Beginning  with  Conversion. 

I.    Some  S  is  P.  I.   Some  S  is  P. 

O.    Some  S  isn't  non-P.  I.    Some  P  is  S. 

O.   Some  P  isn't  non-S. 
PROPOSITION  O. 

Beginning  with  Obversion.  Cannot  be  Converted. 

O.    Some  S  isn't  P  = 

I.    Some  S  is  non-P  — 

I.    Some  non-P  is  S  = 
O.    Some  non-P  isn't  non-S. 


THE   TRADITIONAL   TREATMENT.  139 

Attention  is  directed  to  the  fact  that  by  this  process  of 
alternate  conversion  and  obversion  we  are  able  on  the 
strength  of  a  given  proposition  to  make  assertions  not  only 
about  objects  to  which  the  subject  and  predicate  terms  are 
applicable,  but  about  objects — if  we  assume  them  to  exist — 
to  which  one  or  both  are  wholly  inapplicable  (i.e.,  to 
non-A's  and  non-P's).  We  must,  however,  be  very  careful 
not  to  jump  at  conclusions  of  this  sort.  From  the  proposi- 
tion All  S  is  P  (All  men  are  mortal)  we  can  infer  No  non-P 
is  S  (No  immortals  are  men),  or  All  non-P  is  non-S  (All 
immortals  are  non-human);  but  we  cannot  infer  All  non-S 
is  non-P  (All  non-humans  are  immortals). 

The  principal  difficulty  in  conversion  is  due,  as  we  have 
seen,  to  the  fact  that  a  descriptive  predicate  has  to  be  turned 
into  a  demonstrative  subject  with  the  proper  quantity. 
From  this  difficulty  exclusive  and  exceptive  propositions  are 
free,  since  they  always  distribute  their  predicates.  If  Euro- 
peans alone  are  capable  of  self-government  it  must  be  that 
all  races  capable  of  self-government  are  Europeans.  Indeed 
it  is  a  rather  curious  fact  that  exclusive  and  exceptive 
propositions  imply  something  about  all  the  objects  mentioned 
in  the  predicate  and  about  all  those  not  specially  mentioned 
in  the  subject,  but  not  necessarily  about  all  those  specially 
mentioned  in  the  subject;  so  that  the  objects  to  which  they 
seem  to  call  special  attention  are  those  about  •which  they  say 
the  least.  From  the  supposed  fact  that  Europeans  alone  are 
capable  of  self-government  it  follows,  as  we  have  seen,  that 
all  races  capable  of  self-government  are  European;  it  also 
follows  that  no  non-European  races  are  capable  of  self- 
government;  but  it  does  not  necessarily  follow  that  all 
European  races  are  capable  of  self-government.  Because  of 
this  I  am  inclined  to  think  that  to  transpose  the  subject  and 
predicate  of  an  exclusive  or  exceptive,  proposition  is  an 
analysis  of  meaning  rather  than  a  conversion.  We  cannot 
be  sure  that  European  races  alone  are  capable  of  self-govern- 
ment unless  we  already  know  that  all  the  races  capable  of 


140  IMMEDIATE  INFERENCE. 

self-government  are  European.  The  value  of  the  exclusive 
form  seems  to  lie  in  the  contrast  it  brings  out  between  the 
objects  specially  mentioned  (to  which  the  attribute  in  ques- 
tion at  least  may  belong),  and  the  rest  of  the  class  to  which 
they  belong — the  kind  of  contrast  which  serves  as  the  basis 
for  all  classification. 

The  subject  of  conversion  has  been  discussed  so  far  from 

as  mechanical  a  standpoint  as  possible.  Fol- 
The  treat-  ,  ,  ,  ,  .  .  ,  r 

mentby          lowing  the  older  logicians  we  have  given  rules 

for  the  manipulation  of  words  which  can  be 
followed  blindly. 

In  the  latter  half  of  the  eighteenth  century  Leonard  Euler 
invented,  or  rather  revived,  a  set  of  simple  diagrams  by  which 
the  relations  between  classes  of  objects  could  be  so  easily 
and  so  well  symbolized  that  it  was  no  longer  necessary  to 
follow  rules  mechanically,  or  even  to  remember  them  at 
all.  If  the  members  of  each  class  of  objects  are  supposed 
to  be  enclosed  in  a  circle,  the  visible  relations  of  the  circles 
can  be  relied  upon  to  indicate  the  relations  of  the  classes. 
When  one  class  is  included  in  (or  is  identical  with)  another 
(Proposition  A),  the  circle  S,  supposed  to  enclose  the  mem- 
bers of  the  first,  must  be  drawn  inside  of  (or  coincident  with) 
the  circle  P,  supposed  to  enclose  the  members  of  the 
second;  when  some  members  of  the  first  class  are  also  mem- 
bers of  the  second  (Proposition  I),  at  least  a  part  of  the  circle 
S  must  lie  inside  of  the  circle  P;  when  there  are  some  mem- 
bers of  the  first  class  which  are  not  members  of  the  second 
(Proposition  O),  at  least  a  part  of  the  circle  S  must  lie  outside 
of  the  circle  P;  and  when  no  member  of  the  first  class  is  a 
member  of  the  second  (Proposition  E),  all  of  the  circle  S 
must  lie  outside  of  the  circle  P. 

So  far  it  has  been  the  circle  S  we  have  discussed,  as  wholly 
or  partly  within  or  without  the  circle  P.  But  we  can  neither 
draw  nor  conceive  of  figures  so  constructed  that  a  circle  S 
lies  wholly  or  partly  within  another  circle  P  without  part  of 
P's  area  lying  within  S.  From  '  All  S  is  P  '  (Proposition  A) 


THE   TREATMENT   BY   DIAGRAMS.  141 

or  '  Some  S  is  P '  (Proposition  I)  we  can  therefore  infer 
'  Some  P  is  S  '  (Proposition  I).  Similar  grounds  can  be  found 
in  the  space  relations  of  the  figures  for  the  conversion  of  E 
(No  S  is  P)  into  E  (No  P  is  S) ;  while  the  figure  only  allows 
us  to  convert  O  (Some  S  isn't  P)  into  the  worthless  Proposi- 
tion E,  already  referred  to  (No  P  is  some  S  or  other). 


Thus  when  we  draw  the  diagrams  we  can  convert  without 
reference  to  the  formal  rules,  merely  by  observing  what  the 
relations  of  the  circles  must  be  under  the  given  conditions. 
This  is  a  much  more  natural  and  rational  process  than  to 
blindly  follow  mechanical  rules.  The  only  rule  involved  in 
the  construction  of  diagrams  in  conversion  or  syllogism  is 
this :  Try  to  make  them  represent  the  premise  or  premises  with- 
out at  the  same  time  representing  any  conclusion  you  have  in 
mind.  If  this  cannot  be  done  the  conclusion  follows.  If 
it  can  be  done  it  does  not. 

Euler's  diagrams  have  rendered  great  service  to  logic;  but 
it  must  not  be  forgotten  that  in  using  them  or  any  other 
diagrams  constructed  on  the  same  principle  we  assume  that 
spatial  relations  can  be  relied  upon  to  represent  relations  which 
are  not  spatial.  Diagrams  in  logic  are  metaphors,  and  to 
reason  in  metaphors  is  usually  extremely  dangerous.  Experi- 
ence happens  to  show  that  in  the  case  of  Euler's  diagrams 
the  metaphor  is  not  misleading,  but  we  must  not  forget  -on 
that  account  that  it  is  usually  better  and  safer  when  we  can 
do  so  to  reason  about  the  relations  of  things  themselves 
directly  than  through  the  mutual  relations  of  their  symbols. 


142  IMMEDIATE   INFERENCE. 

The  reason  that  Euler's  diagrams  seem  to  make  logical  rela- 
tions so  clear  is  that  they  appeal  directly  to  the  senses,  and 
that  of  all  the  relations  perceived  by  sense  those  of  space  are 
the  most  constant,  the  most  universal,  and  the  most  easily 
represented.  Almost  every  conceivable  relation  thus  comes 
to  be  symbolized  in  terms  of  space  and  seems  to  be  better 
understood  \vhen  it  is  expressed  in  spatial  language.  It  is 
said  that  every  preposition  once  expressed  a  spatial  relation, 
and  the  same  is  true  of  very  many  words  and  phrases  used 
\vith  reference  to  the  mental  life  (e.g.,  '  apprehend  ',  '  move- 
ment of  thought  ',  '  idea  in,  or  before  the  mind  ',  '  convey  an 
idea  ',  '  express  an  emotion  ',  '  impression  ',  etc!). 

The  great  objection  to  Euler's  diagrams  is  that,  lil.c  the 
rules  which  they  were  intended  to  supplement,  they  apply 
only  to  relations  of  inclusion  or  exclusion  betwee;,  classes. 
Both  are  wholly  inapplicable  to  either  dynamic  or  non- 
dynamic relations  between  different  individuals.  Both, 
therefore,  are  of  service  within  but  a  small  portion  of  the 
whole  sphere  of  thought. 

There  is  no  reason  why  the  term  conversion  should  not 
be  broadened  so  as  to  include  the  transposition  of  subject 

and  predicate  when  the  copula  is  understood  to 
treatmeni.  express  something  other  than  mere  identity  or 

non-identity  of  things  or  classes.  There  are 
many  propositions  in  which  the  subject  and  predicate  name 
two  different  objects  while  the  copula  affirms  or  denies  a 
dynamic  or  non-dynamic  relation  between  them.  The  trans- 
position of  the  subject  and  predicate  of  such  propositions 
might  fairly  be  called  conversion.  The  difficulty  connected 
with  the  traditional  conversion  is  to  settle  the  distribution 
of  the  new  subject;  and  it  arises  from  the  fact  that  a  predi- 
cate used  descriptively  is  turned  into  a  subject  used  demon- 
stratively. With  the  kind  of  conversion  just  mentioned  there 
is  no  such  difficulty,  for  in  dynamic  and  non-dvnamic 
propositions  the  predicate  is  already  used  demonstratively. 
Whatever  mechanical  difficulty  presented  itself  would  come 


A    BROADER    TREATMENT.  143 

from  the  copula.  Sometimes  it  could  remain  unchanged 
and  sometimes  it  would  have  to  be  altered  so  as  to  express 
a  reversed  relation.  If  John  (subject)  is-a-relative-of  (copula) 
James  (predicate),  James  is-a-relative-of  John.  Here  the 
relation,  so  far  at  least  as  it  is  expressed,  is  the  same  for  both 
parties  and  might  be  represented  by  an  arrow  pointed  at  both 
ends:  John  <— >  James;  and  the  proposition  can  be  converted 
by  a  mere  transposition  of  subject  and  predicate.  But  if 
John  is-the-father-of  James  we  cannot  infer  that  James 
is-the-father  of  John.  Here  the  relation  expressed  is  different 
for  the  two  parties  and  should  be  represented  by  an  arrow 
pointing  in  one  direction  only:  John  ->  James;  and  when  we 
convert,  the  copula  must  be  changed,  so  as  to  express  the 
relation  from  the  other  side:  James  is-the-child-of  John, 
James  <-  John. 

When  to  reverse  the  relation  expressed  in  the  copula  and 
when  to  leave  it  alone  is  a  question  that  might  be  seriously 
considered  if  it  were  necessary  or  desirable  to  pay  attention 
merely  to  our  words  and  not  to  what  they  mean.  But  this 
is  not  necessary  or  desirable;  and  the  question  needs  no 
serious  consideration,  for  when  we  pay  attention  to  the  real 
object  of  discourse  and  understand  the  meaning  of  the  words 
used  there  is  no  difficulty. 

Whether  we  use  the  term  conversion  in  this  broad  sense 
or  in  a  still  broader  sense  to  include  statements  about  any 
objects  on  the  strength  of  statements  about  other  objects  in 
which  the  first  objects  were  mentioned,  there  is  no  general 
rule  for  conversion  which  can  be  followed  blindly  and  no  set 
of  symbols  which  is  always  applicable.  The  only  thing  to 
do  is  to  turn  from  mechanical  rules  and  from  symbols  to 
the  things  themselves,  find  out  exactly  what  relations  are 
asserted  of  the  object  spoken  about,  and  then  ask  ourselves 
whether  there  are  not  corresponding  relations  of  other 
objects  mentioned  or  implied  without  which  the  relations 
asserted  could  not  possibly  or  conceivably  exist.  To  do  this 
we  must  imagine  not  only  a  single  state  of  affairs  in  which 


144  IMMEDIATE   INFERENCE. 

the  asserted  relations  exist,  but  many;  to  find  out  whether 
there  is  not  at  least  one  (conceivable,  or  possible,  or  actual, 
as  the  case  may  be)  in  which  the  other  relations  that  seem 
to  be  involved  are  not  really  involved.  This  is  thinking, 
and  no  mechanical  rules  can  save  us  the  trouble. 


CHAPTER  XII. 
MEDIATE   INFERENCE  AND   SYLLOGISM. 

IT  has  already  been  explained  that  mediate  inference  takes 
place  when  we  recognize  some  new  aspect  of  the  total  state 
of  affairs  in  which  alone  all  the  relations  asserted  by  two  or 
more  premises  can  exist  together.  To  put  the  matter  more 
concretely :  Mediate  inference  takes  place  when  we  conclude 
anything  about  the  relations  of  tivo  or  more  objects  to  each  other 
from  the  relations  of  each  to  some  third  object,  the  word 
'  object '  being  used  in  the  broadest  possible  sense  to  include 
qualities  and  relations  as  well  as  things.  From  the  fact  that 
A  is  larger  than  B  and  that  C  is  smaller  than  B  \ve  can  con- 
clude that  A  is  larger  than  C;  and  this  is  mediate  inference. 

No  inference  can  be  drawn  about  the  relations  of  two 
objects  to  each  other,  unless  the  object  with  Tlmlt  tl 
which  each  of  them  is  compared  is  in  both  cases  of  deduction, 
the  same.  From  the  fact  that  A  is  larger  than  B  and  that  C 
is  smaller  than  D,  nothing  can  be  inferred  about  the  rela- 
tions of  A  and  C. 

Moreover  no  inference  can  usually  be  drawn  unless  each 
of  the  two  objects  is  compared  with  the  third  in  the  same 
respect;  unless  the  relations  discussed  are  homogeneous,  or 
at  least  unless  they  belong  to  the  same  unitary  system. 
From  the  fact  that  A  is  larger  than  B  and  that  C  is  lighter 
than  B,  no  inference  can  be  drawn  about  the  relations  of  A 
and  C.  Where  Fuclid  says  "  Things  which  are  equal  to  the 
same  thing  are  equal  to  one  another",  we  must  understand 


146  MEDIATE   INFERENCE   AND   SYLLOGISM. 

him  to  mean:  "  Things  \vhich  are  equal  to  the  same  thing 
in  any  given  respect  are  equal  to  each  other  in  that  respect  ". 
A  may  be  equal  to  C  in  physical  strength,  and  B  equal  to  C 
in  intelligence  without  A  and  B  being  equal  to  each  other 
in  any  respect  whatever.  In  the  same  way  the  line  AB  may 
be  equal  in  length  and  the  line  EF  equal  in  color  to  the 
line  Gil,  without  their 'being  equal  to  each  other  in  either 
one  or  the  other. 

While  no  inference  is  usually  possible  when  the  relations 
dealt  with  are  heterogeneous,  the  inferences  drawn  when  all 
the  relations  under  discussion  are  homogeneous  do  not 
belong  to  formal  logic.  If  A  is  B's  landlord  or  creditor  or 
agent,  and  B  is  C's,  it  is  a  lawyer's  business,  not  that  of  the 
formal  logician,  to  say  whether  A  is  in  any  sense  C's  landlord 
or  creditor  or  agent ;  if  a  substance  D  has  a  chemical  affinity 
for  K,  and  E  for  F,  nobody  but  a  chemist  can  tell  whether 
D  necessarily  has  or  has  not  an  affinity  for  F;  if  G  is  four 
times  as  large  r.s  II,  and  II  is  seven  times  as  large  as  K,  the 
relative  sizes  of  G  and  K  is  a  question  of  mathematics,  and 
the  traditional  field  of  deduction  is  so  limited  that  the  formal 
logician  as  such  is  debarred  from  drawing  a  conclusion. 

In  syllogism  or  the  kind  of  mediate  inference  discussed  in 
formal  logic,  two  of  the  three  relations  usually  involved  in 
the  premises  and  the  conclusion  are  homogeneous,  and  the 
third  is  (or  may  reasonably  be  treated  as)  a  relation  of 
identity.*  If  we  say  '  G  is  four  times  as  large  as  II  and  II 

*  I  say  '  two  of  the  three  relations  -usually  involved  '  because  in  a  sorites 
there  may  be  an  indefinite  number  of  premises.  In  this  case  the  rela- 
tions stated  in  all  the  premises  except  the  last  must  be  relations  of 
identity. 

The  rule  that  two  of  the  three  relations  must  be  homogeneous  and  the 
third  a  relation  of  identity  does  not  exclude  the  case  where  all  three  are 
relations  of  identity,  e.g.,  'A  is  identical  with  B,  and  B  is  identical  with 
(',  then-fore  A  is  identical  \vi:h  C  '.  The  most  serious  objection  that  I 
can  think  of  to  the  rule  as  I  have  stated  it  seems  to  come  from  sucli  cases 
as  thi-:  •  A  is  larger,  taller,  sweeter,  heavier,  better,  prettier  than  B,  B  is 
larger,  etc.,  than  C,  therefore  A  is  larger,  etc.,  than  C  '.  Here  the  rcla- 


LIMITATIONS   OF   DEDUCTION  147 

is  seven  times  as  large  as  K;  therefore  G  is  twenty-eight 
times  as  large  as  K  ',  the  reasoning  belongs  to  mathematics; 
but  when  we  say  '  G  is  four  times  as  large  as  II,  and  H  and 
K  are  one  and  the  same  thing;  therefore  G  is  four  times  as 
large  as  K  ',  the  reasoning  is  syllogistic  and  belongs  to  deduc- 
tive logic.  Similarly  if  we  say  '  A  is  four  miles  due  west  of 
B  and  C  is  three  miles  due  north  of  B,  therefore  A  is  five 
miles  southwest  of  C  ',  the  reasoning  is  geometrical;  but  if 
we  say  '  A  is  four  miles  due  west  of  B,  and  C  is  three  miles 
due  north  of  B  (i.e.,  not  at  all  west  of  B),  therefore  A  and 
C  are  not  the  same  ',  the  reasoning  is  syllogistic.  Or  to  put 
it  somewhat  differently,  if  we  say  '  A  is  two  miles  west  of  B 
and  three  miles  east  of  C,  therefore  B  is  five  miles  east  of  C  ', 
the  reasoning  is  geometrical  or  arithmetical  and  beyond  the 
sphere  of  formal  logic  (not  of  course  '  illogical  ');  but  if  we 
say  '  A  is  two  miles  west  of  B  and  three  miles  east  of  C, 
therefore  something  two  miles  west  of  B  is  three  miles  east 
of  C  (i.e.,  one  and  the  same  thing  is  both  two  miles  west  of 
B  and  three  miles  east  of  C)  ',  the  reasoning  is  syllogistic. 
In  the  examples  of  arithmetical  and  geometrical  reasoning 
here  given  all  the  relations  affirmed  or  denied  were  relations 
of  size,  number,  or  direction;  but  in  the  examples  of  syllo- 
gistic reasoning  this  was  not  the  case.  In  the  first  of  these 
three  examples  of  syllogistic  reasoning  the  second  premise 

tions  are  all  homogeneous  and  no  one  of  them  is  a  relation  of  identity  ; 
and  yet  the  conclusion  seems  to  follow  in  each  case  from  pure  logic,  and 
without  reference  to  any  special  science.  I  suppose  the  answer  to  such 
an  objection  would  be  that  before  we  speak  of  a  thing  as  having  more  of 
a  given  quality  than  anything  else  we  recognize  that  things  can  be  ar- 
ranged in  a  series  with  reference  to  that  quality,  so  that  whatever  goes 
beyond  something  else  goes  still  more  beyond  the  things  which  that  some- 
thing else  goes  beyond.  x\ll  that  is  implied  by  the  use  of  the  compara- 
tive — er  or  more  — .  So  that  when  we  say  '  A  is  taller  than  B,  and  B  is 
taller  than  C,  therefore  A  is  taller  than  C ',  we  might  have  said  'A  is 
taller  than  B,  and  whatever  B  is  taller  than,  C  is  a  thing  that  B  is  taller 
than,  therefore  A  is  taller  than  C  '.  In  the  syllogism  thus  stated  the 
second  premise  asserts  a  relation  of  identity  and  the  rule  holds  good. 


148  MEDIATE   INFERENCE   AND  SYLLOGISM. 

affirmed  a  relation  of  identity  and  thus  made  the  conclusion 
possible;  in  the  second  example  the  conclusion  denied  that 
two  objects  were  identical,  because  they  possessed  incom- 
patible relations;  in  the  third  example  the  conclusion  called 
attention  to  the  fact  that  the  objects  described  in  the  two 
premises  were  identical,  so  that  the  relations  which  they 
affirmed  coexisted,  or  both  belonged  to  the  same  object. 

The  three  examples  of  syllogistic  reasoning  which  we  have 

just  given  to  illustrate  the  difference  between  such  reasoning 

and  that  which  is  not  svllogistic  can  also  be  used 

'  Figures  '. 

to  illustrate  the  difference  between  three  different 
kinds  of  syllogism,  for  there  are  certain  respects  in  which 
they  are  quite  different  from  each  other.  The  examples 
were  these : 

1)  G  is  four  times  as  large  as  H; 

H  and  K  are  one  and  the  same; 
Therefore  G  is  four  times  as  large  as  K. 

2)  A  is  four  miles  due  west  of  B; 

C  is  three  miles  due  north  of  B; 
Therefore  A  and  C  are  not  the  same. 

3)  A  is  two  miles  west  of  B; 

A  is  three  miles  east  of  C: 

Therefore  something  two  miles  west  of  B  is  also  three 
miles  east  of  C. 

In  each  of  the  syllogisms  there  is  a  term  (called  the  Middle 
Term)  which  occurs  in  each  of  the  premises  but  not  in  the 
conclusion;  but  in  the  different  syllogisms  this  middle  term 
does  not  occur  in  the  same  place.  In  the  fin-t  syllogism  the 
middle  term  II  is  the  predicate  of  the  first  premise  and  the 
subject  of  the  second;  in  the  second  the  middle  term  B  is 
the  predicate  of  both  premises;  and  in  the  third  the  middle 
term  A  is  subject  of  both.  This  difference  of  order  is  accom- 
panied by  a  corresponding  difference  of  thought;  and  each 
one  of  the  three  syllogisms  may  be  regarded  as  an  example 


'FIGURES'.  149 

of  one  of  the  three  '  Figures  '  of  the  syllogism,  which  we  are 
about  to  discuss.  Most  logicians  say  that  there  are  four  of 
these  figures;  but  Aristotle  gave  only  three,  and  as  the  fourth 
is  easily  derived  from  the  others  by  a  purely  mechanical 
process,  has  no  special  function  as  distinguished  *rom  the 
others,  and  is  seldom  or  never  used  in  ordinary  reasoning,  it 
may  easily  be  omitted. 


CHAPTER   XIII. 
THE  FIRST  FIGURE  OF  THE  SYLLOGISM. 

IN  the  first  figure  the  reasoning  is  of  this  sort.  One 
premise,  called  the  Major,  asserts  something  about  a  certain 

object  or  certain  objects;  the  other  premise, 
function  called  the  Minor,  points  out  that  one  or  more 

specified  individuals  are  identical  with  some  or 
all  of  these  objects;  and  on  the  strength  of  this  the  Conclu- 
sion makes  the  statement  contained  in  the  major  premise 
with  direct  reference  to  the  individuals  specified  in  the 
minor.  Examples: 

None  of  the  apostles  were  Gentiles; 
Peter  was  an  apostle; 
.  • .  Peter  was  not  a  Gentile. 

Every  one  who  has  consumption  has  tubercular  bacilli; 
This  patient  has  consumption; 
.  •.  This  patient  has  tubercular  bacilli. 

No  Anglo-Saxon  likes  mob  rule; 
Most  Americans  are  Anglo-Saxons; 
.  • .  Most  Americans  do  not  like  mob  rule. 

It  should  be  noticed  that  the  major  premise  (which  in 
each  of  these  examples  is  written  first)  can  affirm  or  deny 
any  sort  of  relation  whatever,  while  the  minor  always  keeps 
saying:  'This  is  he',  'This  is  one  of  them',  'These  are 
some  of  them  '.  We  may  say  if  we  like  that  in  all  typical 

150 


GENERAL   FUNCTION.  151 

examples  of  the  first  figure  the  major  gives  a  rule,  and  the 
minor  points  out  that  a  certain  case  comes  under  it. 

In  this  figure  the  conclusion  merely  makes  a  specific  or 
more  specific  application  of  what  was  said  in  the  major 
premise  to  the  objects  specially  mentioned  in  the  minor. 
To  do  this,  it  substitutes  the  more  specific  term  which  occurs 
in  the  minor  premise  for  the  less  specific  term  which  occurred 
in  the  major;  but  in  the  conclusion  the  general  sense  of  the 
major  premise  and  its  general  arrangement  of  terms  is  pre- 
served. This  is  not  true  of  any  other  figure. 

In  the  two  other  figures  the  distinction  between  major  and 
minor  premise  is  purely  arbitrary,  for  both  premises  deal 
with  the  same  kind  of  relations;  the  conclusion  does  not 
preserve  the  general  sense  of  either;  and  one  arrangement  of 
terms  in  the  conclusion  is  just  as  natural  as  the  other. 

It  should  not  be  overlooked  that  when  the  major  premise 
points  out  a  relation  of  any  sort  between  two  objects  or  sets 
of  objects  the  minor  can  specify  any  or  all  of  the  objects  in 
question,  and  the  specification  is  carried  into  the  conclusion 
regardless  of  whether  these  objects  were  denoted  by  the  sub- 
ject or  by  the  predicate  of  the  major.  The  following,  for 
example,  are  perfectly  valid  syllogisms  in  the  first  figure: 

AUSlavs  hate  all  Semites; 

The  Russians  are  Slavs  and  the  Jews  are  Semites; 
.  • .  The  Russians  hate  the  Jews. 

Oil  and  water  will  never  mix; 
This  is  oil  and  that  is  water; 
.  * .  This  and  that  will  not  mix. 

John  is  beating  Thomas; 
Thomas  is  John's  son; 
.  •  ;  John  is  beating  his  son. 

John  and  Thomas  are  quarreling; 
Thomas  is  John's  son; 
.  * .  John  and  his  son  are  quarreling. 


152          THE   FIRST    FIGURE   OF   THE   SYLLOGISM. 

If  we  use  an  arrow  to  indicate  any  dynamic  or  non-dynamic 
relation  between  two  different  objects  and  three  horizontal 
lines  to  indicate  identity  and  a  bar  across  the  symbol  to 
indicate  the  absence  of  the  relation,  these  four  syllogisms 
would  be  represented  in  this  way : 

Major:  All  Slavs  — »  all  Semites. 

Minors:  Every  Russian  E  a  Slav. 

Every  Jew  =  a  Semite. 
Conclusion:  .  •.  All  Russians  -»  all  Jews. 

Major:  Oil  < — >•  water. 

Minors:  This  =  oil. 

That  E  water.  -\ 

Conclusion:         This  < — >  that. 

Major:  John  ->  Thomas. 

Minor:  Thomas  E  John's  son. 

Conclusion:         John  -»  his  son. 

Major:  John  < — »  James. 

Minor:  Thomas  E  John's  son. 

Conclusion:         John  « — >  his  son.* 

Inference  in  the  first  figure  amounts,  as  has  been  said, 
merely  to  this:  Some  or  all  of  the  individuals  about  which  a 

statement  has  been  made  in  the  major  premise 
Is  there 

real  are  pointed  out  more  specifically  in  the  minor, 

inference  ?  ,       .  .         . 

and    then    m    the    conclusion    the    statement  is 

made  over  again  with  specific  reference  to  these  individuals. 
The  interesting  question  about  it  is  whether  in  such  a  process 

*  When  we  recognize  that  propositions  expressing  relations  between 
different  objects  can  be  treated  by  the  syllogism  we  must  abandon,  for 
such  cases  at  least,  the  old  rule  that  the  major  premise  contains  the 
predicate  of  the  conclusion.  In  the  third  of  these  examples  this  rule 
would  make  what  I  have  called  the  minor  premise — Thomas  is  John's 
son — the  major,  though  it  is  perfectly  obvious  that  it  is  the  other 
premise — John  is  beating  Thomas — whose  general  sense  is  preserved  in 
the  conclusion.  It  is  infinitely  better  to  judge  by  the  meaning  than  by 
the  outward  form. 


IS   THERE   REAL   INFERENCE?  153 

there  is  any  inference  at  all.  Does  not  the  conclusion  merely 
repeat  in  other  words  a  part  of  what  has  been  already  stated 
in  the  major  premise  ?  And  if  so  can  this  be  called  infer- 
ence ?  Mill  and  others  have  maintained  that  it  cannot.  To 
get  a  fair  view  of  the  subject  we  must  consider  three  slightly 
different  sets  of  cases.  Let  us  take  an  example  of  each. 

Peter,  James,  and  John  were  all  Jews; 
Peter  is  one  of  these; 
.  • .  Peter  was  a  Jew. 

All  of  the  apostles  were  Jews; 
Peter  was  an  apostle; 
.  • .  Peter  was  a  Jew. 

Whoever  has  consumption  has  tubercular  bacilli; 
This  patient  has  consumption; 
.  •.  This  patient  has  tubercular  bacilli. 

In  the  first  of  these  examples  no  one  would  maintain  that 
there  is  any  inference.  The  conclusion  merely  repeats  what 
has  been  said  just  as  explicitly  in  the  major  premise. 

In  the  second  example  the  case  is  somewhat  different. 
No  one  who  investigated  the  matter  could  be  sure  that  all 
the  apostles  were  Jews  unless  he  were  first  sure  about  Peter 
and  each  of  the  others  individually,  but  it  would  be  possible, 
nevertheless,  to  make  a  statement  about  all  of  the  apostles 
without  thinking  about  Peter  and  each  of  the  others  indi- 
vidually. If  there  is  inference  in  this  case  it  rests  upon  the 
curious  fact  that,  by  using  such  words  as  '  all  '  and  '  every  ', 
we  can  speak  of  each  of  a  large  number  of  individuals, 
though  we  do  not,  and  cannot,  have  at  once  separate  mental 
images  of  more  than  a  very  few  of  them.  Such  inference  as 
there  is  consists  in  pointing  out  that  the  statement  made 
applies  to  certain  individuals  that  we  may  never  have  thought 
of  when  the  statement  was  made — in  realizing  to  some 
extent  who  or  what  it  was  that  was  spoken  about.  If  we 
adhere  to  our  definition  of  inference  as  the  recognition  of  a 
new  relation  of  things  without  which  the  relations  asserted- 


154          THE   FIRST   FIGURE   OF   THE   SYLLOGISM. 

in  the  premises  could  not  exist,  this  process  is  not  inference, 
for  the  relation  realized  in  the  conclusion  is  not  a  new  one; 
there  is  no  new  fact.  But  if  we  broaden  our  definition  so  as 
to  include  this  realization  of  what  has  been  said,  though 
perhaps  not  realized,  then  of  course  there  is  inference;  there 
is  a  new  thought.  Logicians  who  are  mainly  interested  in 
their  own  mental  processes  are  likely  to  admit  this  broader 
definition;  those  who  are  mainly  interested  in  the  relations 
of  things  are  likely  not  to. 

In  the  third  example  the  case  is  still  different.  When  any 
one  says  that  all  of  the  apostles  were  Jews  he  means  to 
include  each  member  of  a  certain  definite  number  of  indi- 
viduals determined  beforehand.  He  speaks  demonstratively 
of  certain  individuals  as  such.  The  only  question  is  whether 
or  not  he  realizes  as  he  should  the  identity  of  all  the  indi- 
viduals that  -he  speaks  about.  But  when  any  one  says  that 
whoever  has  consumption  is  suffering  from  the  presence  of 
tubercular  bacilli,  he  is  not  pointing  to  certain  definite  indi- 
viduals determined  beforehand.  Rather  he  is  speaking 
descriptively  of  any  individual  who  happens  to  have  con- 
sumption, no  matter  who  he  maybe  or  how  many  there  may 
be  of  them.  To  know  that  whoever  has  consumption  has 
tubercular  bacilli,  one  does  not  have  to  know  first  about 
each  individual  patient  as  such;  he  needs  only  to  know  that 
these  bacilli  are  the  sole  cause  of  the  disease.  When,  there- 
fore, he  puts  the  two  premises  together  and  concludes  that 
some  particular  patient  has  tubercular  bacilli  he  has  gained 
some  knowledge  that  could  not  possibly  have  been  derived 
from  a  mere  analysis  of  the  major  premise.  He  has  reached 
a  new  aspect  of  things— found  a  relation  not  previously 
mentioned- — and  has  undoubtedly  made  an  inference. 

Looking  back  at  the  three  kinds  of  cases,  we  can  see  that 
in  the  first,  where  objects  are  individually  specified  in  the 
major  premise,  the  minor  is  superfluous,  and  in  the  conclu- 
sion there  is  no  real  inference.  In  the  second,  where  a 
certain  definite  number  of  objects  are  mentioned  in  general 


PRINCIPLE   AND   CAUTIONS.  155 

terms  in  the  major,  the  minor  would  be  superfluous  if  we 
realized  all  that  is  said,  and  such  inference  as  there  is  con- 
sists in  realizing  what  is  said.  In  the  third,  where  the  major 
expresses  a  general  law  applicable  to  every  individual  of  a 
certain  kind,  the  minor  is  not  superfluous,  and  in  the  con- 
clusion there  is  real  inference. 

From  all  that  has  been  said  it  is  evident  that  the  principle 
upon  which  we  reason  in  the  first  figure  is  as  follows:  What 

is  true  of  an  object  specified  in  one  war  is  true  of 

,  .  .,    ,  .  ,  ,t  Principle 

the   same  object  specified  in  any  other  way.      it  we   and 

,  .          .....  .        .          cautions. 

omit  the  case  in  which  the  major  premise  is  a 

singular  proposition,  the  principle  amounts  to  this:  What  is 
stated  in  a  universal  proposition  is  slated  of  every  object  to  which 
the  subject  term  is  applicable;  or,  less  technically,  What  is  said 
to  be  true  of  every  member  of  a  group  (or  of  every  object  which 
possesses  a  given  relation)  is  said  about  each  one  of  them, 
even  though  each  is  not  separately  thought  of  when  the  statement 
is  made. 

So  much  for  the  principle.  In  applying  it  we  must 
observe  certain  cautions.  In  the  first  place,  if  the  major 
premise  speaks  only  of  certain  unspecified  members  of  a  group 
— i.e.,  if  the  major  is  particular — we  cannot  be  sure  that  any 
of  the  objects  named  in  the  minor,  though  members  of  the 
group,  are  objects  spoken  of  in  the  major;  and  consequently 
no  conclusion  can  be  drawn. 

It  is  true  that  some  animals  are  fierce,  and  it  is  also  true 
that  all  mice  are  animals;  but  it  is  not  true  that  mice  are 
fierce.  If  such  a  conclusion  did  happen  to  be  true  in  any 
one  case,  that  would  not  make  it  follow  from  the  premises; 
for  a  conclusion  does  not  follow  unless  we  can  be  absolutely 
certain  that  whenever  premises  of  that  kind  are  true  that  kind 
of  conclusion  must  be  true  also. 

If  we  use  a  number  of  small  circles  to  represent  animals 
of  various  kinds,  and  let  a  plain  stroke  drawn  through  a 
circle,  (}) ,  indicate  that  the  animal  is  fierce,  and  a  stroke  with 
a  bar  across  it,  (J) ,  indicate  that  it  is  not  fierce,  the  major 


156          THE   FIRST    FIGURE   OF   THE   SYLLOGISM. 

premise  gives  this  picture:  o  ({)  O  (j)  (j)  O  Some  are  said  to 
be  fierce,  and  of  some  nothing  is  said ;  so  some  of  the  circles 
are  marked  with  a  plain  stroke  and  some  are  left  unmarked. 

If  now  we  indicate  mice  by  thickened  dots,  we  must  put 
all  the  dots  within  the  circles  to  indicate  what  is  stated  in 
the  minor  premise,  that  each  mouse  is  identical  with  some 
animal ;  but  as  there  may  be  animals  which  are  not  mice,  we 
must  leave  some  circles  without  dots,  thus:  o  o  O  O  If 
it  afterwards  turns  out  that  every  animal  is  a  mouse,  we  can 
fill  in  the  remaining  circles. 

Now  if  we  indicate  in  a  single  set  of  figures  everything 
which  has  been  asserted  and  remember  this  rule:  Do  not  put 
more  marks  than  you  have  to  in  any  one  circle,  we  get  such  a 
diagram  as  the  following:  o  (})({)  O  0  O 

Here  dots  and  plain  strokes  do  not  coincide,  but  there  is 
nothing  in  the  diagram  to  indicate  that  they  cannot.  That 
would  be  Indicated  by  drawing  a  crossed  stroke  (meaning 
not-fierce)  through  every  dot,  thus:  o  (j)  (J)  (f)  <£  O  The 
figure  as  it  stands  merely  means  that  there  is  no  evidence 
to  show  that  any  dot  (mouse)  must  possess  a  plain  stroke 
(fierceness).  Whenever  the  major  premise  is  particular  it  is 
possible  to  construct  such  a  diagram. 

If  in  the  example  given  the  major  premise  had  been  uni- 
versal, every  circle  would  have  been  marked,  so  that  it  would 
have  been  impossible  to  avoid  putting  the  dots  where  they 
would  also  be  marked;  and  so  the  diagrams  would  have  in- 
dicated the  conclusion  that  all  mice  are  fierce:  <$>  §  <$>  (j) 

If  the  major  premise  is  not  particular,  but  the  minor  is, 
that  is,  if  the  minor  says  that  some  members  of  a  second 
group  belong  to  the  group  spoken  of  in  the  major  but  does 
not  say  which  members  of  the  second  group  these  are,  then 
we  can  conclude  that  what  was  said  in  the  major  premise 
was  said  of  some  members  of  the  group  named  in  the  minor, 
but  we  cannot  possibly  say  which  members  they  are.  The 
objects  cannot  be  designated  any  more  definitely  in  the  con- 
clusion than  they  were  designated  in  the  premise.  If  all 


PRINCIPLE   AND   CAUTIONS.  157 

young  animals  like  play  and  some  mice  are  young  animals, 
we  can  conclude  that  some  mice  like  play,  (J)  (f)  §  •  ,  but  we 
cannot  conclude  that  all  mice  like  play  or  that  any  particular 
mouse  likes  it.  In  other  words,  if  the  minor  premise  is 
particular,  the  conclusion  must  be  particular  also.  If  we 
have  no  definite  information  to  begin  with,  syllogistic  manip- 
ulation will  not  supply  it. 

Putting  together  what  has  been  said  about  the  two 
premises,  our  FIRST  CAUTION  is  this:  In  the  first  figure  if  the 
major  premise  is  particular,  no  conclusion  can  be  drawn;  if 
the  minor  is  particular,  the  conclusion  must  be  particular. 
This  caution  can  be  stated  less  mechanically  and  without 
regard  to  figure  or  distinction  of  premises  as  follows: 

i)  A  relation  can  belong  to  some  members  of  a  group  without 
belonging  to  all  the  members,  to  any  given  member,  or  to  any  one 
of  a  given  group  of  members. 

The  phrase  '  to  all  the  members  '  is  really  superfluous  ;  for 
no  relation  could  belong  to  each  member  without  belonging 
to  a  given  member.  What  is  true  of  all  mice  must  be  true 
of  this  mouse.  The  last  words  of  the  caution — "or  to  any 
one  of  a  given  group  of  members  " — are  necessary  in  order  to 
exclude  a  particular  conclusion  as  well  as  a  singular  or  uni- 
versal when  the  major  premise  is  particular. 

The  principle  on  which  we  reason  in  the  first  figure  is 
quite  as  applicable  when  the  major  premise  is  negative  as 
when  it  is  affirmative.  The  proposition  '  No  men  are  per- 
fect '  states  something  about  every  man,  not  about  no  man. 
It  means  that  every  man  is  without  perfection,  and  if  we 
know  Socrates  to  be  a  man,  it  is  applicable  to  Socrates. 
If  we  represent  the  proposition  by  a  diagram,  we  may  cross 
our  strokes  to  indicate  that  the  objects  represented  have  not 
the  quality  in  question;  but  the  strokes  must  be  drawn 
through  every  circle,  to  indicate  that  every  man  is  described, 
^  (j)  (J),  and  the  circle  that  stands  for  Socrates  must  be 
marked  with  the  rest. 

But  when  the  minor  premise  in  the  first  figure  is  negative  it 


158          THE   FIRST   FIGURE   OF   THE   SYLLOGISM. 

does  not  come  under  the  principle,  and  no  conclusion  can  be 
drawn.  If  we  know  that  all  the  apostles  were  Jews,  it  will 
not  tell  us  anything  about  Job's  race  to  say  that  he  was  not 
an  apostle.  The  function  of  a  minor  premise  in  this  figure 
is  to  point  out  particularly  some  of  the  things  spoken  about 
in  the  major,  and  if  an  object  is  not  one  of  those  spoken 
about  in  the  major,  then  nothing  has  been  said  about  it  one 
way  or  the  other. 

Clear  as  this  is,  there  is  a  strong  tendency  in  such  cases 
to  draw  a  negative  conclusion,  e.g.,  The  apostles  were  Jews; 
Job  was  not  an  apostle;  therefore  Job  was  not  a  Jew. 
The  caution  against  yielding  to  this  tendency  might  run  as 
follows: 

2)  To  say  that  something  is  true  of  certain  objects  does  not 
imply  that  it  is  false  of  others. 

The  same  tendency  to  draw  negative  conclusions  where 
no  conclusion  at  all  should  be  drawn  is  found — though  it  is 
not  so  strong — where  the  minor  premise  is  particular.  If 
we  are  told  that  no  men  are  perfect  and  that  some  rational 
beings  are  men,  we  have  a  right  to  conclude  that  some 
rational  beings — namely,  those  that  are  men — are  not  perfect ; 
but  we  have  no  right  to  conclude  that  some  rational  beings 
— namely,  those  that  are  not  men — are  perfect.  To  do  so 
is  to  ignore  the  caution  just  given.  It  also  involves  the 
other  blunder  of  interpreting  '  some  are  '  to  mean  '  some 
are  and  some  are  not '.  The  statement  that  some  rational 
beings  are  men  gives  us  no  valid  reason  for  believing  that 
they  are  not  all  men.  Both  blunders  are  covered  by  the 
caution.* 

Here  is  a  set  of  diagrams  for  the  benefit  of  any  one  who 
may  wish  to  compare  them  with  his  own.  If  we  wish  to 
include  negative  minors,  we  may  draw  a  short  stroke  through 
one  side  of  the  circles  to  indicate  something  outside  of  the 

*  The  first  caution  covers  fallacies  of  illicit  minor  ami  undistributed 
middle  as  they  occur  in  the  tirst  figure  ;  the  second  caution  covers 
fallacies  of  illicit  major  in  the  same  figure. 


A 

§  §  (J)       Conclusion  A 

A 

<j>  4  <j> 

E 

A 

(j)  (j)  O  O 

none 

A 

(J)  (j)  O  O 

«          « 

I 

(J)  (j)  <l>   « 

I 

I 

^  ^  ^    * 

0 

I 

(j)  0  . 

none 

I 

<j>  0   • 

"           " 

E 

({)(])»• 

"           " 

E 

(J)  (J)  •    . 

«           <  i 

et 

cetera. 

PRINCIPLE   AND   CAUTIONS.  i;? 

group  that  the  circles  stand  for,  or  something  that  does  not 
have  their  qualities.* 

Major  A  and  minor  A 
11      E   " 
"      I    " 
«<       Q    " 

"      A    " 


T 
Q 

A 


*  If  we  wished  to  distinguish  in  our  diagrams  between  syllogisms  m 
which  the  major  premise  describes  objects  as  they  are  in  themselves  and 
those  in  which  it  tells  of  some  causal  or  other  relation  between  objects, 
we  could  indicate  the  latter  in  some  such  way  as  the  following,  u.'-ing 
the  arrow  to  indicate  the  relation  : 

O)  (O 

Every  Slav  hates  every  Semite     O  f     :»->     •<  O 

O)  (O 

O 

Every  Russian  is  a  Slav     Q 
O 

(O 
Every  Jew  is  a  Semite       •<  Q 

(  O 

©)  (O 

Therefore  every  Russian  hates  every  Jew,      Q  ^    yi>-*     J  Q 

O  )  (  O 

That  is  to  say,  The  Slavs,  including  all  the  Russians,  hate  the  Semiles, 
including  all  the  Jews. 

Every    Slav   hates    every   Semite,  and    some  Russians    are  Slavs   and 

O)  (O 

some  Jews  are  Semites       Q  V     m->     •<  O 
G  )  (  O 

In  the  text  I  have  treated  universal  propositions  as  though  they  were 
nothing  more  nor  less  than  statements  about  every-  member  of  a  certain 


160          THE   FIRST   FIGURE   OF   THE   SYLLOGISM. 

group  of  objects,  and  have  omitted  any  reference  to  the  causal  relation 
•which  they  so  often  imply.  (See  above,  p.  109.) 

The  principle  and  cautions  can  be  easily  restated  so  as  to  take  account 
of  this  causal  relation,  as  follows  : 

Any  object  or  relation  (S)  which  possesses  or  involves  a  given  rela- 
tion (M)  possesses  or  involves  every  other  relation  (P)  which  that  rela- 
tion (M)  involves,  provided  that  M  really  (i.e.,  necessarily  or  always) 
involves  it. 

The  fact  that  an  object  or  relation  (S)  does  not  possess  or  involve  a 
relation  (M)  which  involves  another  relation  (P)  is  no  evidence  that  the 
object  or  relation  (S)  does  not  possess  or  involve  this  other  relation  (P,. 

The  first  paragraph  covers  the  rule  and  the  more  important  part  of 
the  first  caution  ;  the  second  covers  the  second  caution.  To  cover  the 
rest  of  the  first  caution  we  must  add  that  a  statement  about  some  un- 
designated  member  or  members  of  a  group  of  objects  (S)  will  not  enable 
us  to  say  anything  about  any  particular  one  of  them. 

Here  is  an  example  of  the  sort  of  causal  connections  I  speak  of  : 

Going  to  war  involves  danger  for  the  soldier. 

Danger  for  the  soldier  involves  distress  for  his  family. 

.-.  Going  to  war  involves  distress  for  the  soldier's  family. 

Each  of  the  diagrams  in  the  text  is  intended  to  represent  at  least  one 
sample  of  every  object  mentioned  in  either  premise,  and  to  preserve 
the  distinction  between  those  that  are  described  in  a  given  respect  and 
those  that  are  not.  I  have  tried  to  make  the  illustrations  as  concrete  as 
possible  by  using  closed  figures — circles  or  dots — to  represent  things, 
and  lines  drawn  through  them  to  indicate  attributes.  When  the  sense 
is  once  understood  these  circles  are  not  so  good  as  a  matter  of  practical 
convenience  as  simple  letters  written  one  alter  tne  other  with  the  under- 
standing that  the  first  letter  stands  for  a  thing  and  those  that  come  after 
it  for  attributes.  AB  would  thus  mean  that  all  A's  have  the  attribute 
1?  (i.e.,  are  B's).  A,  AB  would  mean  that  some  A's  have  the  attribute 
B.  A,  ABC,  BC,  would  mean  that  some  A's  are  B  and  all  B's  are  C, 
and  that  therefore  some  A's  are  C.  When  these  letters  are  used,  a 
stroke  over  a  letter  indicates  the  absence  of  the  attribute  in  question. 
ABC,  BC  means  that  all  A's  are  non-B,  and  all  non-B's  are  C,  and 
therefore  all  A's  are  C. 

When  we  use  these  letters  it  is  easy  to  get  from  pictorial  representa- 
tions to  algebraic.  A  =  AB  means  that  every  A  has  the  attribute  B,  i.e., 
that  every  A  is  also  B. 

The  pictorial  representations  most  used  are  Euler's.  These  do  not 
attempt  to  represent  individual  objects  or  to  preserve  the  distinction 
between  things  and  attributes  ;  but  deal  with  the  mutual  relations  of 
classes.  As  the  diagrams  are  drawn  on  precisely  the  same  principle 


PRINCIPLE   AND   CAUTIONS. 


161 


for  all  the  figures  (including  the  fourth)  there  is  no  denying  their  con- 
venience for  any  one  who  has  to  work  out  a  set  of  problems.  Here  are 
some  of  the  diagrams  for  the  first  figure. 


Major  A 
Minor  A 
Conclusion  A 


Major  A 
Minor  I 
Conclusion  I 


Major  A 
Minor  E 
Conclusion  — 


Major  E 
Minor  A 
Conclusion  E 


Major  E 
Minor  I 
Conclusion  O 


Major  I 
Minor  A 
Conclusion  — 


The  dotted  lines  are  used  to  indicate  doubt  as  to  where  the  circle  or 
the  part  of  the  circle  in  question  should  fall. 


CHAPTER   XIV. 
THE   SECOND   FIGURE   OF   THE   SYLLOGISM. 

IN  this  figure  each  premise  describes  an  object  or  set  ot 

objects,  and  from  the  nature  of  the  two  descrip- 
Tunction  .  ,      .  ,,         .      . 

and  general    tions   the    conclusion    tells  whether  or    not    the 
cautions.  ,  .  .  ,        .      .      .,  ,        , 

objects  are  identical  with  each  other. 

The  man  that  came  to  my  house  was  tall  and  thin; 
The  man  that  went  to  your  house  was  short  and  fat 

(i.e. ,  not  tall  and  thin); 
.  • .  The  man  that  came  to  my  house  is  not  the  man  that 

went  to  your  house. 

Crows  do  not  sing; 
This  bird  sings; 
.  • .  This  bird  is  not  a  crow. 

Whales  suckle  their  young; 
Fishes  do  not : 
.  • .  Whales  are  not  fishes. 

The  second  and  third  of  these  examples  differ  from  the 
first  in  this  respect :  In  the  fin.t,  two  given  objects  are  com- 
pared, and  we  conclude  that  they  are  not  identical;  in  the 
second  a  given  object  is  compared  with  a  class  of  objects, 
and  we  conclude  that  it  does  not  belong  to  the  class — that 
it  is  not  the  kind  of  thing  to  which  the  class-name  applies; 
in  the  third  two  classes  of  objects  are  compared.  In  the 
first  case  we  are  concerned  with  identification  in  the  nar- 
rowest sense  of  the  term;  in  the  others  with  classification. 
In  the  general  description  of  the  figure  I  have  mentioned 
only  the  identification  because  it  is  the  more  fundamental 

162 


FUNCTION   AND   GENERAL   CAUTIONS.  163 

and  the  classification  really  depends  upon  it.  If  \ve  could 
not  distinguish  between  individual  objects,  we  could  not 
distinguish  between  classes.  To  say  that  whales  are  not 
fishes  is  to  say  that  there  is  not  any  whale  which  is  identical 
with  any  fish.  To  classify  is  thus  merely  to  distinguish 
between  individuals  in  groups,  and  the  principles  by  which 
we  distinguish  classes  are  nothing  more  than  those  by  which 
we  distinguish  individuals. 

In  this  figure,  therefore,  both  premises  are  concerned  with 
descriptive  relations,  and  the  conclusion  with  a  relation  of 
identity.* 

The  next  thing  to  be  noticed  about  the  figure  is  that  the 
two  premises  must  describe  their  objects  in  the  same  respect. 
If  I  describe  the  man  I  saw  as  tall,  and  you  describe  the  one 
you  saw  as  agreeable,  the  descriptions  indicate  absolutely 
nothing  about  the  identity  of  the  men. 

But  even  when  both  premises  describe  their  objects  in  the 
same  respect  a  conclusion  is  not  always  possible.  If  each 
of  two  persons  had  met  a  tall  man  named  Smith,  they  would 
not  necessarily  have  met  the  same  man.  Two  Dromios  or 
two  atoms  of  hydrogen  might  have  innumerable  points  of 

*  For  the  purposes  of  this  figure  propositions  which  in  themselves  are 
not  strictly  descriptive  are  treated  as  such.  When  we  conclude,  for 
example,  that  Newhaven  and  New  Haven  are  different  cities  because 
one  is  on  the  road  from  Paris  to  London,  and  the  other  on  the  road  from 
New  York  to  Boston,  the  geographical  or  spatial  relations  of  each  ot 
them  to  the  adjacent  cities  are  practically  regarded  as  a  part  of  the 
city  itself.  The  distance  between  Newhaven  and  London  or  Paris  is 
a  spatial  relation  and  belongs  as  much  to  London  or  Paris  as  to 
Newhaven.  But  when  it  serves  to  distinguish  Newhaven  from  New 
Haven  it  is  treated  as  though  it  belonged,  like  its  size  or  its  history, 
to  Newhaven  itself.  For  this  reason  we  make  the  word  Newhaven 
the  subject  of  the  sentence  in  which  the  facts  are  expressed.  We  do 
not  say  '•  London  is  a  usual  terminus  for  persons  traveling  from  Paris 
and  Newhaven",  or  "A  good  way  to  reach  London  from  Paris  is 
through  Newhaven  ",  or  '•  London  is  so  far  from  Newhaven  and  so  much 
farther  from  Paris  byway  of  Newhaven".  What  the  syllogism  in- 
volves is  not  the  distance  of  London  or  Paris  as  such,  but  all  of  them  in 
so  far  as  they  characterize  Newhaven. 


1 64        THE   SECOND    FIGURE   OF   THE   SYLLOGISM. 

resemblance  and  yet  be  two.  As  the  points  of  resemblance 
between  two  complex  things  increase,  the  probability  that 
the  things  are  really  identical  also  increases;  but  no  amount 
of  resemblance  can  supply  theoretically  absolute  proof  of 
such  identity.  The  prisoner  in  the  dock  might  bear  every 
resemblance  to  the  man  who  was  seen  reeling  on  the  street 
the  night  before  and  yet  possibly,  though  not  probably,  be 
a  different  man.  We  could  be  absolutely  certain  of  their 
identity  only  if  the  reeling  man  had  been  arrested  at  the  time 
and  never  lost  sight  of  for  a  moment  until  he  was  placed  in 
the  dock. 

The  fact  is  that  the  identity  of  two  things  involves  a  great 
deal  more  than  mere  resemblance,  no  matter  how  complete 
the  resemblance  may  be.  Consequently,  though  we  can 
often  prove  that  things  are  not  identical  from  the  fact  that 
they  are  dissimilar,  we  can  never  prove  that  they  are  identical 
from  the  fact  that  they  are  similar.  If  men  are  mortal  and 
angels  are  not  mortal,  it  follows  that  men  are  not  angels; 
but  if  men  are  mortal  and  horses  are  mortal,  it  does  not 
follow  that  men  are  horses.  In  this  figure  negative  conclu- 
sions alone  are  valid. 

There  is  no  logical  blunder  more  frequent  than  to  conclude 
that  because  things  are  alike  they  are  necessarily  the  same. 
Flour  is  white,  says  the  child;  what  I  see  all  over  the  ground 
is  white;  therefore  what  I  see  all  over  the  ground  is  flour. 

Good  dollars  are  silvery-looking  discs  bearing  a  certain 

stamp ; 

This  is  a  silvery-looking  disc  bearing  that  stamp; 
.  • .  This  is  a  good  dollar. 

Benevolent  people  smile  affably; 
This  man  smiles  affably; 
.  • .  This  man  is  benevolent. 

All  Pis  M; 
All  Sis  M; 
.  • .  All  S  is  P. 


FUNCTION  AND  GENERAL  CAUTIONS.      165 

But  what  the  child  sees  on  the  ground  is  snow,  not  flour, 
and  sometimes  our  silver  disc  is  counterfeit,  and  the  smiling 
stranger  a  brute.  S  is  not  always  P. 

The  logical  trouble  comes  when  we  mistake  probabilities 
for  certainties.  In  practical  life  it  is  usually  better  to  take 
an  occasional  counterfeit  coin  than  to  insist  upon  testing 
them  all,  better  to  be  deceived  in  a  character  occasionally 
than  to  refuse  all  intercourse  with  one's  fellows  until  they 
prove  their  right  to  be  trusted,  better  to  bow  to  a  stranger 
than  to  cut  a  friend.  But  a  good  rule  of  conduct  when  we 
must  act  in  a  hurry  is  not  necessarily  a  good  rule  of  conduct 
or  thought  when  we  have  time  to  be  careful.  The  bank 
teller  must  be  on  the  watch  for  counterfeit  money,  the  em- 
ployer of  a  confidential  clerk  must  look  behind  his  face, 
and  the  sheriff  should  be  sure  of  his  man.  In  the  same 
way,  as  students  of  deductive  logic  we  must  reject  all  con- 
clusions that  do  not  follow  with  absolute  necessity  from  the 
premises.* 

*  The   significance   of  this  fallacious  reasoning  A  A  A  in  the  second 
figure  may  become  clearer  if  we  show  its  relations  to  the  first  figure. 
In  the  second  figure  we  say 

All  Y  is  Z 

All  X  is  Z 

.-.  All  X  is  Y 

Now  if  we  could  convert  the  first  premise  simply,  i.f.,  without  alter- 
ing the  quantity,  we  should  get  a  perfectly  valid  syllogism  in  the  first 
figure  : 

All  Z  is  Y        <f>  <$>  (j> 
All  X  is  Z 
.-.  All  X  is  Y 

But  we  cannot  convert  the  premise  simply.  All  we  can  say  is  that  some 
Z  is  Y,  and  from  this  major  premise  no  conclusion  can  be  drawn, 
(j)  O  O 

If  we  happened  to  know  not  only  that  some  Z  is  Y,  but  that  most  Z  is 
Y,  we  might  conclude  that  X  is  probably  Y. 

Most  silvery  looking  discs  bearing  a  certain  stamp  are  good  dollars. 

This  is  a  silvery  looking  disc  bearing  that  stamp. 

.-.  This  is  probably  a  good  dollar. 

Even  as  a  rule  for   hurried  action  it  is  not  wise  to  draw  affirmative 


1 66        THE   SECOND   FIGURE   OF   THE   SYLLOGISM. 

We  have  seen  that  in  this  figure  no  affirmative  conclusion 
can  be  drawn — similar  things  are  not  necessarily  identical. 
But  how  about  the  negative  conclusion  ?  Can  we  say  with 
any  more  certainty  that  dissimilar  things  are  not  identical  ? 
Is  not  the  tadpole  of  last  summer  identical  with  this 
summer's  frog,  the  bright-winged  bird  of  the  spring  with  the 
sober-looking  one  of  the  summer,  the  grub  of  one  month 
with  the  butterfly  of  the  next,  Saul  the  persecutor  with  Paul 
the  apostle  ?  On  the  other  hand,  no  one  can  suppose  that 
the  tadpole  is  identical  with  the  later  bird,  or  the  grub  with 
Paul,  or  even  that  a  tadpole  seen  this  morning  is  identical 
with  a  perfect  frog  seen  this  noon.  The  fact  is  that  objects 
can  be  distinguished  from  each  other  by  their  qualities  or 
relations  only  when  these  are  different  at  one  and  the  same 
instant;  so  that  if  the  objects  are  not  observed  simultaneously 
we  cannot  distinguish  them  by  their  qualities  or  relations 
unless  we  believe  these  latter  to  be  so  permanent  that  they 
cannot  be  wholly  changed  in  the  time  which  has  elapsed 
between  the  two  observations.  What  qualities  or  relations 
are  relatively  permanent  and  what  are  not  we  can  learn  only 
through  experience,  without  a  constant  appeal  to  which 
logic  is  perfectly  helpless.* 

To  sum  up,  the  PRINCIPLE  on  which  we  reason  in  the 
second  figure  is  that  Dissimilar  objects  are  not  identical;  and 
these  are  the  CAUTIONS: 

3)  Similarity  does  not  prove  identity,  f 

4)  Dissimilarity  does  not  prove  non-identity  if  the  olject  might 
have  changed. 

conclusions  in  the  second  figure  unless  we  have  reason  to  believe  that 
(lie  converse  of  the  major  premise  is  usually  true.  In  other  words,  the 
.>nly  possible  justification  fur  such  reasoning  in  the  second  figure  is  ii.und 
/n  the  iact  that  it  sometimes  repre.-ents  a  fairly  good  induction  in  the 
first  figure. 

*  Of  course  it  is  only  things  that  change  and  still  retain  their  identity. 
JSiiie  is  not  like  yellow  now,  and  never  will  be. 

t  This  caution  covers  the  fallacy  of  undistributed  middle  as  it  occurs 
in  the  second  figure. 


QUANTITY   IN   THE   SECOND   FIGURE.  167 

5)  Different  descriptions  do  not  imply  dissimilarity  unless  the 
relations  described  are  incompatible. 

So  far  our  examples  have  all  dealt  with  universal  or  singu- 
lar propositions,  and  no  difficulties  have  arisen 
from  questions  of  quantity.     It  is  clear  that  from   ^^gity 
universal    or   singular    premises    a    universal    or  second 
singular  conclusion  can  be  drawn;  but  can  we 
draw  any  conclusion  at  all  from  particular  premises  ? 

First,  when  both  premises  are  particular.  If  some  mem- 
bers of  Congress  have  blue  eyes  and  some  lovers  of  literature 
have  brown  eyes,  i.e.  ,  have  not  blue  eyes,  what  inference 
can  be  drawn  ?  It  is  clear  enough  that  certain  members  of 
Congress,  namely,  those  with  blue  eyes,  are  not  identical  with 
certain  lovers  of  literature,  namely,  those  with  brown  eyes. 
Using  the  sign  =  to  indicate  identity  and  ^  to  indicate  non- 
identity,  we  can  make  such  a  diagram  as  this: 

Congressmen.          Lovers  of  Literature. 


o  o 

o  o 

meaning  that  no  one  of  the  described  congressmen  is  iden- 
tical with  anyone  of  the  described  lovers  of  literature.  But 
for  all  we  know,  each  one  of  the  described  congressmen  may 
be  identical  with  one  of  the  undescribed  lovers  of  literature, 
and  vice  versa,  e.g.,  the  first  in  one  column  with  the  third  in 
the  other,  and  so  on.  It  might  be  that  every  congressman 
was  a  lover  of  literature  and  every  lover  of  literature  a  con- 
gressman, in  spite  of  the  fact  that  a  blue-eyed  congressman 
is  not  a  brown-eyed  lover  of  literature. 

To  put  the  matter  somewhat  differently.      From  the  fact 
that  certain  S's  are  not  identical  with  certain   P's,  it  by  no 
means  follows  that  certain  S's  are  not  P's  at  all.      Suppose 
every  S  to  be  a  P  as  indicated  below: 
S's.  P's. 


1 68        THE   SECOND    FIGURE   OF   THE   SYLLOGISM. 

The  first  S  is  identical  with  the  first  P,  but  for  that  very 
reason  it  cannot  possibly  be  identical  with  the  second  or  the 
third.  If  there  are  in  all  one  hundred  different  S's  and  one 
hundred  different  P's,  and  if  each  of  the  S's  is  identical  with 
one  of  the  P's,  then  there  are  ninety-nine  different  P's  with 
which  that  particular  S  is  not  identical.  Jones  the  congress- 
man is  identical  with  Jones  the  literary  man,  but  not  with 
Smith  or  Brown. 

As  long  as  there  are  two  or  more  S's  it  must  necessarily 
be  true  that  certain  S's  and  certain  P's  are  not  identical,  and 
it  does  not  make  any  difference  whether  every  S  is  a  P,  or 
no  S  is  a  P,  or  some  S's  are  P  and  some  are  not.  Hence  the 
inference  we  seem  to  drawyroflz  two  particular  premises  in  the 
second  figure — that  certain  S's  are  not  identical  with  certain 
P's — does  not  follow  from  these  premises  any  more  than  from 
any  others  in  which  several  S's  are  mentioned.  It  is  equiva- 
lent to  the  mere  truism  that  no  one  S  can  be  identical  with 
more  than  one  P.  It  is  something  we  might  have  known 
long  before  we  knew  anything  about  the  special  facts  stated 
in  the  premises.  It  is  practically  no  inference  whatever  from 
these  premises  and  we  may  as  well  say  that  from  such 
premises  no  inference  can  be  drawn. 

When  one  premise  is  particular  and  the  other  singular  the 
case  is  much  the  same.  If  we  have  been  told  that  some  of 
the  masqueraders  at  a  ball  were  tall  and  if  we  know  that 
John  is  short,  we  can  be  sure  that  John  was  not  one  of  these 
tall  masqueraders.  We  can  say  if  we  like  that  there  were 
certain  persons  there  with  whom  John  was  not  identical ;  but 
we  know  that  already  if  we  happen  to  know  that  there  were 
more  persons  than  one  present.  It  doesn't  depend  at  all 
upon  the  question  of  height.  This  inference  is  thus  worth- 
less; and  no  other  can  be  drawn. 

When  one  premise  is  universal  the  case  is  different.  If 
everybody  at  the  ball  was  tall  and  John  is  short,  we  know 


QUANTITY   IN   THE   SECOND   FIGURE. 


169 


that  he  is  not  identical  with  any  one  of  them,  i.e.  ,  he  was 
not  there.  Similarly  if  we  had  been  told  that  every  one  at 
the  ball  was  tall  and  that  there  are  some  members  of  the 
club  who  are  not  tall,  we  could  be  sure  that  there  are  some 
members  of  the  club  who  are  not  to  be  identified  with  any 
one  who  was  at  the  ball,  i.e.  ,  some  members  of  the  club 
were  not  at  the  ball. 

Club  =  S.        At  the  ball  =  P. 


o 

o  1  4> 

On  the  other  hand  we  could  not  be  sure  that  some  of  those 
at  the  ball  were  not  members  of  the  club.  If  some  S's  are 
M  and  no  P's  are  M,  or  if  some  S's  are  not  M  and  all  P's 
are  M,  it  follows  that  some  S's  are  not  P's;  but  it  does  NOT 
follow  that  some  P's  are  not  S's,  for  it  may  be  that  each 
of  the  P's  is  identical  with  one  of  the  undescribed  S's.  The 
S's.  P's.  S's.  P's 


Cj) 


f 


o  4> 

O  I  (j) 

reasoning  is  valid  only  if  you  arrange  your  conclusion  so  as 
to  have  for  its  predicate  the  term  which  occurred  in  the 
universal  premise.  In  the  technical  language  of  the  syllo- 
gism :  The  major  premise  (i.e.,  the  one  containing  the  predi- 
cate of  the  conclusion)  must  be  universal.  The  difference 
between  concluding  that  some  S's  are  not  P's  and  that  some 
P's  are  not  S's  may  become  clearer  if  we  remember  that 
Proposition  O  cannot  be  converted. 

When  both  premises  are  universal  it  is  clear  enough  that 
a  universal  conclusion  can  be  drawn;  and  of  course  it  makes 
S's.  P's.  S's.  P's. 


170        THE   SECOND   FIGURE   OF   THE   SYLLOGISM. 

no  difference  which  of  the  premises  is  affirmative  or  negative, 
so  long  as  the  quality  of  the  two  is  different. 

Putting  all  this  together  we  can  add  another  CAUTION: 

6)  We  cannot  say  that  any  S's  are  not  P's  unless  each  of  the 
S's  in  question  is  different  from  every  P '.*  To  put  it  some- 
what differently,  Evidence  sufficient  to  prove  that  some  S  s  are 
not  P's  may  not  be  sufficient  to  prove  that  some  P's  are  not  S  sy 
and  vice  versa. 

The  general  principle  of  the  figure  and  the  caution  respect- 
ing quantity  are  worked  out  together  in  the  following  formula 
which  a  student  may  use  if  he  likes  instead  of  the  separate 
statements: 

If  all  tJie  members  of  one  group  differ  in  a  given  respect  from 
all  the  members  of  another,  then  no  member  of  either  group  is  a 
member  of  the  other.  If  some  members  of  one  group  differ  from 
all  the  members  of  another,  then  l/ierc  are  some  members  of  the 
first  group  which  are  not  members  of  the  second ;  but  it  does  not 
follow  that  there  are  members  of  the  second  which  are  not  mem- 
bers of  the  first.  The  mere  Jact  that  some  members  of  one 
group  differ  from  some  members  of  another  proves  that  those 
particular  individuals  are  not  identical,  but  it  does  not  prove  that 
any  member  of  cither  group  is  not  al\o  a  member  of  the  other. 

*  This  caution  covers  the  fallacy  of  illicit  major  in  the  second  figure. 
Illicit  minor  is  covered  in  the  second  hgure  as  in  the  first  by  the  first 
caution. 


CHAPTER  XV. 

THE  THIRD  FIGURE  OF  THE  SYLLOGISM. 

IN  this  figure  one  premise  asserts  that  a  certain  object  pos- 
sesses (or  does  not  possess)  a  given  relation,  and  the  other 

premise  asserts  that  this  same  object  possesses  (or 

Purpose, 
does  not  possess)  another  given  relation,  and  on   principle, 

the  strength  of  these  premises  the  conclusion  as-   g-eneral 
serts  that  the  presence  (or  absence)  of  one  of  the 
relations  sometimes  coincides  with  the  presence  (or  absence) 
of  the  other—  e.g.  : 

Shakspeare  was  perfectly  sane; 

Shakspeare  was  a  genius; 

.  • .  Some  geniuses  (one  at  least)  are  perfectly  sane, 
or  Some  perfectly  sane  persons  are  geniuses. 

Sin  is  evil ; 
Sin  exists; 
.  • .  Something  evil  exists. 

The  ancient  Stoics  were  not  enlightened  by  the  Scrip- 
tures ; 

These  Stoics  believed  in  God  ; 

.  • .  Some  persons  not  enlightened  by  the  Scriptures  have 
believed  in  God. 

This  figure  is  used  mainly  to  disprove  sweeping  statements 
or  alleged  general  laws,  by  displaying  cases  to  which  they 
will  not  apply.  If  any  one  maintains  that  every  genius  is  a 
morbid  degenerate,  we  can  disprove  the  statement  by  calling 


172          THE   THIRD   FIGURE   OF   THE   SYLLOGISM. 

his  attention  to  the  fact  that  Shakspeare  or  Goethe  or  Plato 
was  a  man  of  undoubted  genius  yet  perfectly  free  from  every 
trace  of  morbid  degeneracy.  If  he  maintains  that  in  God's 
world  no  evil  can  exist,  we  need  only  point  to  sin.  If  he 
maintains  that  through  the  Scriptures  alone  can  God  be 
known,  it  is  only  necessary  to  remind  him  of  the  Stoics. 

In  this  figure  more  than  in  any  other  the  machinery  of  the 
syllogism  seems  very  cumbersome  and  unnecessary.  In  or- 
dinary speech  and  thought  we  consolidate  the  two  premises 
into  one  statement :  Shakspeare  was  a  genius  •  and  yet  not 
morbid  -^,  Sin  is  an  evil  •  and  yet  exists  •+-,  The  Stoics 
believed  in  God  cj)  cf)  § ,  though  not  enlightened  by  the 
Scriptures  -^  -^  -^-. 

The  PRINCIPLE  on  which  we  reason  is  evidently  this  : 

A  single  actual  case  in  which  two  positive  or  negative  relations 
coincide  proves  that  they  are  not  incompatible, 

In  the  examples  here  given  Shakspeare's  freedom  from 
morbidness  and  the  Stoics'  ignorance  of  the  Scriptures  may 
be  regarded  as  negative  relations.  As  applied  to  these  two 
cases  the  principle  means  that  freedom  from  morbidness  is  not 
inconsistent  with  genius,  and  vice  versa;  that  ignorance  of 
the  Scriptures  is  not  inconsistent  with  a  knowledge  of  God, 
and  vice  versa. 

When  both  relations  are  negative  a  conclusion  can  be 
drawn  quite  as  well  as  when  one  or  both  are  positive.  From 
the  fact  that  stones  are  neither  virtuous  nor  vicious  -fa  -^f  -fa 
we  can  prove  that  the  absence  of  one  of  these  qualities  does 
not  necessarily  preclude  the  absence  of  the  other,  and  thus 
disprove  the  statement  that  everything  in  the  world  must  be 
one  or  the  other.* 

*  The  old  syllogistic  rule  says  :  From  two  negative  premises  no  conclu- 
sion can  be  drawn;  but  in  the  third  figure  the  rule  is  evaded  by  obvertin^ 
one  or  both  premises.  So  that  if  we  say  '  Stones  aren't  virtuous,  and 
stones  aren't  vicious  '  we  cannot  draw  a  conclusion,  but  if  we  say  stones 
aren't  virtuous  and  stones  are  not-vicious  we  can  !  Conclusions  do  not 
depend  upon  the  form  of  words  in  which  the  premises  are  stated,  but 
upon  the  real  state  of  affairs  to  which  they  point;  yet  when  we  consider 


PURPOSE,   PRINCIPLE,    AND   GENERAL   CAUTION.     173 

Our  conclusion  in  the  example  given  does  not  depend  upon 
the  mere  fact  that  there  are  no  such  things  as  virtuous  or 
vicious  stones,  for  if  there  were  no  stones  at  all  this  would 
still  be  a  fact,  though  the  conclusion  would  not  follow  ;  but 
upon  the  fact  that  there  are  stones  which  are  neither  virtuous 
nor  vicious.  To  state  the  case  more  generally  :  The  conclu- 
sion does  not  depend  upon  the  fact  that  objects  with  the  rela- 
tion in  question  do  not  exist,  but  upon  the  fact  that  objects  do 
exist  without  the  relation. 

This  last  statement  suggests  what  is  involved  in  the  prin- 
ciple of  the  figure  as  I  have  stated  it,  but  what  cannot  be  too 
much  emphasized,  that  the  cases  from  which  our  conclusions 
are  drawn  must  actually  exist.  We  cannot  prove  that  a  good 
man  may  come  to  grief  by  Colonel  Newcome,  that  a  brave 
man  may  murder  his  wife  by  Othello,  that  good  nature  will 
not  save  us  from  cruelty  by  Arthur  Donnithorne,  that  wounds 
will  not  destroy  existence  by  the  heroes  of  Valhalla,  or  that 
a  pumpkin-shell  may  be  transformed  into  a  chariot  by  the 
adventure  of  Cinderella.  From  particular  cases  in  one  uni- 
verse we  cannot  prove  the  compatibility  of  relations  in 
another. 

The  first  CAUTION  to  be  observed  in  using  this  figure  is 
— put  technically — that  its  conclusion  is  always  particular.  If 
all  men  are  mortal  and  all  men  are  bipeds,  we  can  be  sure  that 
so  far  as  men  are  concerned  these  two  attributes  coincide, 
but  this  does  not  prove  that  every  mortal  creature  has  two 
legs  or  that  angels  and  all  other  bipeds  are  sure  to  die.  In 
other  words,  the  fact  that  certain  objects  possess  each  of  several 
positive  or  negative  relations  does  not  prove  that  other  objects  may 
not  possess  one  ivithoui  the  other  or  exist  without  either.  Or 
more  briefly : 

7)  Any  number  of  coincidences  between  relations  will  no/ 
prove  that  they  coincide  always. 

this  state  of  affairs  there  is  a  sense  in  which  we  can  say  that  premises  in 
this  figure  from  which  a  conclusion  can  be  drawn  must  both  be  affirma- 
tive in  meaning,  no  matter  what  their  form.  See  the  next  paragraph. 


174          THE   THIRD   FIGURE   OF   THE   SYLLOGISM. 

The  briefer  statement  is  less  comprehensive,  but  it  will 
cover  any  case  that  is  likely  to  arise.* 

In  this  figure  as  in  the  second  we  must  be  careful  not  to  be 
confused  by  negative  relations.  From  the  fact  that  all  M's 
are  P,  and  that  no  M's  are  S,  we  can  infer  that 
relations.  some  P's  are  not  S  ;  but  we  cannot  infer  that  some 
S's  are  not  P. f  From  the  Pope  we  may  perhaps 
prove  that  there  are  infallible  mortals,  but  not  that  there  are 
fallible  immortals.  It  takes  the  Devil  for  that.  The  sixth 
caution  or  its  corollary — "Evidence  sufficient  to  prove  that 
some  S's  are  not  P's  may  not  be  sufficient  to  prove  that  some 
P's  are  not  S's" — is  one  which  we  tend  to  ignore  or  mis- 
understand continually.  Altogether  the  best  way  to  observe  it 
without  confusion,  whether  we  are  reasoning  in  the  third  fig- 
ure or  in  one  of  the  others,  is  to  put  our  premises  affirmatively, 
with  the  negative  element,  when  there  is  one,  in  the  predi- 
cate (i.e.,  to  obvert  negative  premises  and  conclusions). 
When  we  say  that  there  are  infallible  mortals  or  that  there 
are  fallible  immortals,  our  meaning  is  much  clearer  and  the 
distinction  between  the  two  statements  is  much  more  obvious  | 

*  Tliis  caution  covers  illicit  minors  in  the  third  figure.      Put  in  terms 

of  causal  relations  the  caution  is  this  : 

A  single    coincidence    proves  the  compatibility  of    relations,    but  r,o 

number  of  coincidences  can  prove  their  necessary  connection. 

•j-  This  caution  covers  illicit  majors  in  the  third  figure  as  well  as  in  the 

second. 

\  The  statement  in  this  form  has  moreover  the  advantage  of  directing 

attention  to  the  fact  that  we  are  talking  alxjut  real  things.      ("See  top  of 

p.  173.)  The  diagrams  in  the  text  seem  to  me  to  accent  the  affirmative 
element  which  reasoning  in  the  third  figure 
particularly  involves,  as  well  as  to  guard 
against  the  confusion  referred  to  in  the  text 
letter  than  Euler's.  Students  always  find 
it  difficult  to  see  why  this  figure  does  not 
mean  that  some  P's  are  not  S  as  well  as  that 
some  S's  are  not  P.  But  if  we  represent  S 
by  a  vertical  stroke  and  P  by  a  horizontal 

the  distinction  between  M  which   is  S  but  not  1'  -(j>  and  M  which  is  P 

but  not  S  -{•>-  is  obvious,  and  with  it  the  distinction  between  S  not-P  -£+ 

and  P  not-S  -- 


QUANTITY    OF   THE   PREMISES.  175 

than  wh'en  we  say  that  some  mortals  are  not  fallible  or  that 
some  fallible  beings  are  not  mortal. 

By  the  coincidence  of  two  relations  we  mean  that  they  both 
belong  to  the  same  individual.  Whether  they  do  or  not  is 

primarily,  of  course,  a  matter   of  observation   in 

Quantity 

each  particular  case  :   but  when  the  coincidence   of  the 
...  .     .  .        .    ..         .   .  .  premises. 

of  the  relations  must  be  inferred  by  putting  to- 
gether statements  about  the  existence  of  each  \ve  must  re- 
member one  more  CAUTION  : 

8)  Two  different  relations  can  belong  to  individuals  of  the 
same  class  without  belonging  to  the  same  individual,  unless  at 
least  one  of  the  m  belongs  to  every  individual  in  ike  class* 

If  \ve  know  that  this  particular  X  is  both  Y  and  Z,  we  know 
of  course  that  V  and  Z  coexist.  If  \ve  kno\v  that  every  X  is 
Y  and  every  X  is  Z,  we  can  be  sure  that  each  X  is  both  Y 
and  Z  ;  if  we  know  that  every  X  is  Y  and  that  some  X  is  Z, 
we  can  be  sure  that  some  X  or  other  is  both  Y  and  Z  ;  but 
if  we  only  know  that  some  X's  or  other  are  Y  and  that  some 
X's  or  oilier  are  Z,  we  cannot  be  sure  that  Y  and  Z  ever  belong 
to  the  same  X.  This  is  what  is  meant  in  this  figure  by  the 
technical  rule  that  from  two  particular  premises  no  conclusion 
can  le  drawn.  The  technical  rule  should  have  added  that 
from  a  particular  premise  and  a  singular  premise  in  the  third 
figure  no  conclusion  can  be  drawn  ;  foi  it  does  no  good  t> 
know  which  particular  X's  are  Y  so  long  as  we  do  not  know 
which  are  Z. 

The  principle  and  all  the  cautions  can  be  put  together  in 
such  a  general  statement  as  this  : 

The  coincidence  of  relations — whether  positive  or  negative — 
proves  that  they  are  compatible,  but  it  does  not  prove  that  cither 
of  them  involves  the  other,  or  thai  the  absence  of  one  is  com- 
patible either  with  the  presence  or  with  the  absence  of  the  other. 
Moreover  t/.e  fact  that  two  relations  belong  to  objects  of  the  same 
class  will  not  prove  thai  they  belong  to  the  same  objects  unless 
at  least  one  of  them  belongs  to  all  the  objects  in  the  class. 
*  This  covers  undistributed  middies  in  the  third  figure. 


CHAPTER   XVI. 
THE  ALLEGED   FOURTH   FIGURE.* 

So  long  as  the  various  figures  of  the  syllogism  were  dis- 
tinguished by  the  mere  arrangement  of  terms  rather  than  by 
the  relations  involved  in  the  reasoning,  it  seemed 
of  the  reasonable  that  there  should  be  a  figure  to  repre- 

sent every  possible  arrangement.  Consequently 
to  the  three  figures  which  we  have  discussed,  and  which  were 
all  that  Aristotle  recognized,  Galen  (131-200  A.D.)  added 
a  fourth.  The  arrangement  of  terms  in  each  is  as  follows  : 


First  Figure. 
MP 

Second  Figure. 
PM 

Third  Figure. 

MP 

Fourth  Figure. 

PM 

SM 

SM 

MS 

MS 

SP 

SP 

SP 

SP 

The  four  figures  cover  every  possible  permutation  of  the 
terms. 

Reasoning  in  the  fourth  figure  outside  of  exercises  in 
formal  logic  is  extremely  rare.  Beyond  mere  questions  of 
whether  one  class  includes  or  excludes  members  of  another, 

Three  ways  it  has  no  significance;  and  though  it  is  easy  to 
of  dealing  °  .  °  / 

with  it.          arrange  problems  in  such  a  way  that  they  will  fall 

within  the  figure,  they  lose  most  of  their  meaning  when  so 
arranged  and  seem  strained  and  unnatural.  Nevertheless 
one  ought  to  know  how  to  deal  with  the  problems  when  they 
arise.  There  are  three  ways  of  doing  this.  The  first  is  to 
disregard  their  meaning  and  solve  them  by  means  of  a  set 
of  purely  mechanical  rules.  These  rules  are  equally  applica- 
ble to  all  four  of  the  figures  ;  but  inasmuch  as  we  have  tried 

*  This  chapter  is  not  essential. 

176 


THREE   WAYS   OF   DEALING   WITH   IT. 


177 


to  get  along  without  them — or  at  least  to  interpret  them — in 
the  other  figures,  it  seems  a  pity  to  take  refuge  in  them  now.* 
The  second  way  of  dealing  with  syllogisms  in  the  fourth 
figure  is  to  assume  that  they  are  concerned  merely  with  rela- 
tions of  inclusion  or  exclusion  between  a  number  of  classes, 
all  of  which  are  assumed  to  exist, 
and  then  to  test  them  by  Euler's 
diagrams.  For  example, 

Some  P's  are  M's  ; 
All  M's  are  S's  ; 
.-.  Some  S's  are  P's. 

The  conclusion  follows  ;  for  we  cannot  possibly  put  the  circle 

M  within  the  circle  S,  and  part  of  _. .., 

the  circle  P  within  the  circle  M, 
without  some  part  of  the  area  of 
S  falling  within  the  circle  P. 

Some  P's  are  M's  ; 
No  M's  are  S's  ; 
.  •.  Some  S's  are  not  P's. 

*  The  rules,  as  stated  by  Jevons,  are  as  follows  : 

1.  Every  syllogism  has  three  and  only  three  terms.      These  terms  are 
called  the  major  term,  the  minor  term,  and  the  middle  term. 

2.  Every  syllogism  contains  three  and  only  three  propositions.    These 
propositions  are  called  the  major  premise,  the  minor  premise,  and  the 
conclusion. 

3.  The  middle  term  must  be  distributed  once  at  least,  and  must  not  be 
ambiguous. 

4.  No  term  must  be  distributed  in  the  conclusion  which  was  not  dis- 
tributed in  one  of  the  premises. 

5.  From  negative  premises  nothing  can  be  inferred. 

6.  If  one  premise  be  negative,  the  conclusion  must  be  negative  ;  and 
vice  versa,  to  prove  a  negative  conclusion  one  of  the  premises  must  be 
negative. 

From  the  above  rules  may  be  deduced  two  subordinate  rules,  which  it 
will  nevertheless  be  convenient  to  state  at  once. 

7.  From  two  particular  premises  no  conclusion  can  be  drawn. 

8.  If  one  premise  be  particular  the  conclusion  must  be  particular. 

These   rules  are  not  absolutely  reliable  unless  we    assume   that   the 
objects  denoted  by  each  term  in  the  syllogism  exist. 


178  THE   ALLEGED   FOURTH   FIGURE. 

The  conclusion  does  not  follow,  for  we  can  construct  a 
diagram  which  represents  the  premises  without  representing 
the  supposed  conclusion. 

The  third,  and  of  course  the  best,  way  of  dealing  with 
syllogisms  in  the  fourth  figure  which  we  are  called  upon  to 
test  is  to  try  to  give  them  a  rational  interpretation  and  thus 
work  in  the  light.  When  we  come  to  interpret  such  syl- 
logisms we  shall  find  that  we  must  regard  them  as  concerned 
either  with  the  relations  between  classes  which  we  have  just 
discussed  or  with  the  relations  peculiar  to  some  one  of  the 
three  other  figures,  to  which  the  syllogism  in  question  cai.  be 
'  reduced  '  by  converting  the  conclusion  or  one  or  both  of 
the  premises. 

If  we  turn  back  to  the  table  which  shows  the  arrangement 
of  terms  in  each  figure,  it  is  easy  to  see  that  by  converting 
the  major  premise  of  a  syllogism  in  the  fourth  figure  we 
Formal  Set  tne  arrangement  of  terms  found  in  the  third  ; 

reduction.  jjy  converting  the  minor  we  get  that  found  in  the 
second ;  and  by  converting  the  conclusion  or  by  converting 
both  premises  we  get  that  found  in  the  first.  It  is  thus 
formally  possible  to  interpret  the  fourth  figure  by  any  one 
of  the  three  others  ;  and  so  long  as  we  do  not  attempt  to 
test  a  universal  conclusion  by  the  third  figure  (which  is 
itself  incapable  of  giving  such  a  conclusion)  or  an  affirmative 
conclusion  by  the  second  (which  never  gives  it),  that  is  to 
say,  so  long  as  we  do  not  ask  a  figure  to  test  a  kind  of  con- 
clusion that  it  is  itself  unable  to  draw,  it  does  not  make  the 
slightest  difference,  as  far  as  the  formal  process  is  concerned, 
which  of  the  first  three  figures  we  use  to  test  a  syllogism  in 
the  fourth.  If  it  is  valid,  there  are  always  at  least  two  of 
the  first  three  figures  in  which  the  conclusion  can  be  proved. 
l»!it  since  the  second  and  the  third  figures  both  have  the 
limitations  just  referred  to,  any  one  who  merely  wants  an 
t-asy  formal  test  will  save  himself  some  thinking  by  making 
it  a  rule  to  test  every  argument  in  the  fourth  figure  by  re- 
ducing it  to  the  first.  In  doing  this  he  may  assume  that 


FORMAL   REDUCTION.  179 

no  syllogism  in  the  fourth  figure  is  valid  unless  the  conclu- 
sion can  be  obtained  either  by  converting  a  conclusion  which 
can  be  drawn  in  the  first  figure  from  the  same  premises,  or 
by  reasoning  in  the  first  figure  from  the  converse  of  the 
premises.  In  other  words,  if  you  have  to  test  a  syllogism  in 
the  fourth  figure,  ask  first  whether  it  is  not  merely  a  syl- 
logism in  the  first  figure  with  the  conclusion  converted  (or 
converted  and  weakened,  i.e. ,  O  from  E  as  well  as  I  from  A). 
If  it  is,  the  reasoning  is  usually  assumed  to  be  valid.  If  it  is 
not,  then  convert  the  premises,  if  they  can  be  converted 
(remembering  that  A  must  be  converted  into  I  and  that  O 
cannot  be  converted  at  all),  and  see  whether  the  conclusion 
in  question  will  not  follow  from  them  according  to  the  prin- 
ciple of  the  first  figure  without  the  \iolatiuii  of  any  caution. 
If  it  will,  the  syllogism  in  the  fourth  figure  is  assumed  to  be 
valid  ;  but  if  the  syllogism  will  not  stand  either  of  these  tests, 
it  certainly  is  not  valid. 
Here  are  some  examples  : 

(1)  All  P's  are  M's  ; 
All  M's  are  S's  ; 

.  • .    Some  S's  are  P's. 

According  to  the  rule  just  laid  down  this  syllogism  is  valid, 
because  from  the  premises  as  they  stand  we  can  reason  in  the 
first  figure  to  the  conclusion  '  All  P's  are  S's  ',  which  by 
conversion  gives  the  conclusion  in  question  '  Some  S's  are 
P's'. 

The  following  syllogism  is  not  valid: 

(2)  All  P's  are  M's; 
All  M's  are  S's; 

.-.    All  S's  are  P's; 

because  (i)  the  universal  conclusion  is  more  than  we  can  get 
by  converting  "  All  P's  are  S's  ",  and  (2)  if  we  convert  the 
premises  we  get 

Some  M's  are  P's  ; 

Some  S's  are  M's  ; 


I  So  THE   ALLEGED   FOURTH   FIGURE. 

from  which  we  cannot  draw  any  conclusion  whatever  without 
disregarding  the  caution  which  says  that  from  a  statement 
about  some  undesignated  members  of  a  class  we  cannot  infer 
anything  about  any  designated  member  or  any  one  of  a  desig- 
nated set  of  members. 

(3)  No  gods  are  Americans  ; 
All  Americans  are  mortal ; 

.  • .   Some  mortals  are  not  gods. 

To  reduce  this  syllogism  to  the  first  figure  we  must  convert 
the  premises,  e.g., 

No  Americans  are  gods  ; 
Some  mortals  are  Americans  ; 
.  •  .   Some  mortals  are  not  gods. 

This  reasoning  is  perfectly  valid,  and  thus  our  original  syl- 
logism is  vindicated. 
One  more  example  : 

(4)  All  students  are  human  ; 

No  human  beings  like  torture  ; 

.  • .   Some  beings  that  like  torture  are  not  students. 

This  syllogism  can  be  proved  valid  like  the  others  by  means 
of  the  first  figure,  though  when  we  try  to  '  reduce  '  it  a  diffi- 
culty immediately  confronts  us,  for  the  conclusion  of  the 
syllogism  is  a  particular  negative  proposition  which  cannot 
be  converted,  and  when  we  convert  the  premises  the  con- 
clusion will  not  follow,  viz.: 

Some  human  beings  are  students  ; 

No  beings  that  like  torture  are  human  ; 

.• .   Some  beings  that  like  torture  are  not  students. 

To  reason  in  this  way  violates  this  caution  :  '  To  say  that 
something  is  true  of  certain  objects  does  not  imply  that  it  is 
false  of  others ',  i.e.,  to  say  that  some  (or  all)  human  beings 
are  students  does  not  imply  that  beings  who  like  torture  and 
are  therefore  not  human  are  not  students. 

We  cannot  convert  the  conclusion,  we  cannot  prove  it  by 
converting  the  premises,  and  yet  the  reasoning  is  valid  !  I 


FORMAL   REDUCTION.  181 

gave  this  example  in  order  to  bring  outthe  difference  between 
converting  a  conclusion  and  obtaining  that  conclusion  by 
converting  something  else.  From  the  premises  in  question, 
'  No  human  beings  like  torture '  and  '  All  students  are 
human',  \vecan  reason  in  the  first  figure  to  the  conclusion 
that  'No  students  like  torture'.  Converting  this  we  get 
'No  beings  that  like  torture  are  students  ',  and  if  this  is  true 
it  is  necessarily  true  also  that  '  Some  beings  that  like  torture 
are  not  students  '.  The  fact  that  this  is  less  (if  it  really  is  less) 
than  we  might  have  inferred  does  not  interfere  with  the  valid- 
ity of  the  inference.  That  is  to  say,  the  conclusion  given  in 
the  example  can  be  obtained  by  converting  the  conclusion  in 
the  first  figure,  though  the  conclusion  in  the  first  figure  can- 
not be  obtained  by  converting  the  conclusion  given  in  the 
example.  We  were  testing  the  fourth  figure  by  the  first,  not 
the  first  by  the  fourth  ! 

I  have  spoken  at  some  length  about  this  reduction  to  the 
first  figure  because  it  is  the  traditional  method  of  testing  syl- 
logisms not  only  in  the  fourth  figure  but  in  the  second  and 
third  as  well.  But  an  undiscriminating  reduction  to  the  first 
figure  has  no  more  value  for  thought  than  a  mechanical  use  of 
cut-and-dried  '  rules  of  the  syllogism  ',  and  probably  has  much 
less  value  than  the  use  of  the  diagrams.  Our  thought  grows 
mechanical  all  too  soon,  and  it  is  a  pity  for  logic  of  all  studies 
to  hasten  the  process.  If  we  are  really  to  work  in  the  light 
in  testing  syllogisms  of  the  fourth  figure,  their  '  reduction  ' 
must  be  accompanied  by  their  interpretation,  and  the  figure 
to  which  we  reduce  them  must  be  determined  by  the  inter- 
pretation— not  by  mere  convenience  for  tormal  manipula- 
tion.* 

*  Looking  back  at  example  No.  I,  let  us  fill  it  out  as  follows  : 

All  persons  a  hundred  miles  above  the  surface  of  the  earth  (P's)  are 
organic  beings  beyond  the  pressure  of  the  atmosphere  (M's). 

All  organic  beings  beyond  the  pressure  of  the  atmosphere  (M's)  become 
greatly  swollen  (S's). 

From  these  premises  it  is  easy  enough  to  draw  the  conclusion  in  the 
first  figure  that  all  persons  a  hundred  miles  above  the  surface  of  the  earth 


182  THE   ALLEGED   FOURTH    FIGURE. 

(P's)  become  greatly  swollen  (S);  meaning  that  if  a  person  should  reach 
such  an  altitude  the  intra-organic  pressures,  not  counteracted  by  pres- 
sure from  without,  would  cause  him  to  swell  up.  But  the  conclusion  in 
the  fourth  figure,  that  some  things  which  become  greatly  swollen  (S's) 
are  persons  a  hundred  miles  above  the  surface  of  the  earth  (P),  looks 
more  like  a  description  of  some  actually  existing  swollen  objects  than 
like  an  account  of  what  would  happen  under  certain  purely  hypothetical 
circumstances.  It  cannot  be  turned  into  hypothetical  form,  and  the  im- 
plication that  such  things  as  swollen  persons  a  hundred  miles  above  the 
surface  of  the  earth  exist  is  certainly  much  stronger,  to  say  the  least, 
than  in  the  conclusion  drawn  according  to  the  first  figure.  In  so  far  as 
it  involves  such  an  implication  the  conclusion  in  the  fourth  figure  is  of 
course  misleading  and  fallacious,  for  we  have  no  right  to  confuse  hypo- 
thetical and  real  conditions.  (See  page  109,  note.) 

Example  No.  3  can  be  reduced  as  we  have  seen  to  the  first  figure,  but 
if  the  two  universal  propositions  which  compose  the  premises  are  inter- 
preted as  stating  causal  relations  no  conclusion  is  possible;  that  is  to  say, 
from  the  fact  that  deity  involves  not  being  an  American  and  that  being 
an  American  involves  mortality  we  cannot  draw  any  conclusion.  The 
conclusion  follows  only  if  we  assume  that  Americans  exist.  It  is  in  the 
third  figure  that  the  syllogism  is  most  natural  and  most  significant,  e.g.: 
All  Americans  are  mortal  and  none  of  them  are  gods;  therefore  '  Some 
mortals  are  not  gods  '.  The  Americans,  not  gods  or  mortals  as  such,  are 
evidently  the  concrete  individuals  irom  a  knowledge  of  whom  the  con. 
elusion  is  drawn. 

In  the  case  of  example  No.  4  the  conclusion  drawn,  '•  Some  beings  that 
like  torture  are  not  students  ",  stands  the  traditional  test  of  reduction  to — 
or  rather  deduction  from — the  first  figure;  but  so  far  as  it  implies  that 
beings  who  like  torture  exist,  it  does  not  follow  from  the  premises.  Ev  n 
the  universal  conclusion,  "  No  beings  that  like  torture  are  students  ", 
is  likely  to  be  misleading,  because  the  causal  relation  between  being  a 
student  and  disliking  torture  is  so  remote  that  the  statement  looks  a  good 
deal  like  a  description  of  actually  existing  beings  that  like  torture.  It 
would  have  been  better  to  say  that  if  any  being  likes  torture  it  is  not 
a  student.  It  is  this  which  follows  from  the  premises. 

The  sum  and  substance  then  of  what  I  have  said  in  criticism  of  this 
figure  is  this:  It  obscures  the  real  relations  under  discussion,  and  in  doing 
so  is  likely  to  lead  to  erroneous  conclusions  besides  tempting  us  to 
work  in  the  dark  by  a  rule  of  thumb. 


CHAPTER     XVII. 
OTHER   DEDUCTIVE   ARGUMENTS. 

WE  have  already  distinguished  between  categorical  propo- 
sitions and  those  which  are  hypothetical  or  dis- 
junctive.     The      syllogisms      discussed      so     far 
involved  only  categorical  propositions,  but  there 
are   also   syllogisms  in  which  hypothetical   and   disjunctives 
have  a  place. 

Hypothetical  syllogisms  run  as  follows  : 

If  A  is  B,  C  is  D  ;     If  a  man  is  a  Christian,  he  forgives  ; 
A  is  B  ;  J.  S.  is  a  Christian  ; 

.  •  .  C  is  D.  .  •  .  J.  S.  forgives. 

If  A  is  B,  C  is  D ;     If  a  man  is  a  Christian,  he  forgives; 
C  is  not  D  ;  J.  S.  does  not  forgive  ; 

.  •  .  A  is  not  B.         .  '  .  J.  S.  is  not  a  Christian. 

A  Hypothetical  Syllogism  is  thus  one  in  which  the  major 
premise  is  a  hypothetical  proposition  and  the  minor  a  cate- 
gorical. 

The  first  pair  of  examples,  in  which  the  state  of  affairs 
mentioned  in  the  consequent  part  of  the  major  premise  is 
proved  to  exist,  are  said  to  be  constructive  or  of  the  modus 
ponens ;  the  second  pair,  in  which  the  state  of  affairs  men- 
tioned in  the  antecedent  part  of  the  major  is  proved  not  to 
exist,  are  said  to  be  destructive  or  of  the  modus  fallens. 
According  to  this  a  syllogism  might  be  constructive  though 

183 


184  OTHER   DEDUCTIVE   ARGUMENTS. 

its  conclusion  were  negative,  and  destructive  though  affirma- 
tive, e.g.  : 

If  A  is  B,  C  is  not  D; 

A  is  B; 
.  • .  C  is  not  D  (Constructive). 

If  A  is  not  B,  C  is  not  D; 
C  is  D; 

.  • .  A  is  B  (Destructive). 

Hypothetical  syllogisms  look  like  an  entirely  new  sort; 
but  the  novelty  lies  altogether  in  the  verbal  form,  not  in  the 
relations  expressed;  for  we  have  seen  (page  109)  that  the 
relations  expressed  by  hypothetical  propositions  can  be 
expressed  about  as  well  in  universal  categorical  propositions, 
and  when  the  hypothetical  major  premise  of  a  hypothetical 
syllogism  is  put  into  categorical  form  only  a  slight  change 
is  required  in  the  minor  to  make  the  syllogism  also  cate- 
gorical. Making  these  changes,  we  get 

A  state  of  affairs  in  which  A  is  B  is  a  state  of  affairs 

in  which  C  is  D; 

This  is  a  state  of  affairs  in  which  A  is  B; 
.  • .  This  is  a  state  of  affairs  in  which  C  is  D. 
A  Christian  forgives; 
J.  S.  is  a  Christian; 
.  • .  J.  S.  forgives. 

A  state  of  affairs  in  which  A  is  B  is  a  state  of  affairs  in 

which  C  is  D; 

This  is  a  state  of  afiairs  in  which  C  is  not  D; 
.  • .  This  is  a  state  of  affairs  in  which  A  is  not  B. 
A  Christian  forgives; 
J.  S.  does  not  forgive; 
.  • .  J.  S.  is  not  a  Christian. 

The  constructive  hypothetical  syllogism  thus  resolves  itself 
into  an  ordinary  syllogism  in  the  first  figure;  the  destructive 
into  one  in  the  second. 

The   formal    rule  for   hypothetical    syllogisms   is  that  the 


HYPOTHETICAL   SYLLOGISMS.  185 

minor  premise  must  either  affirm  the  antecedent  of  the  hypo- 
thetical proposition  in  the  major  (as  in  the  first  two  of  these 
last  examples)  or  deny  the  consequent  (as  in  the  second  two). 
In  the  first  of  the  following  examples  we  commit  the  Fallacy 
of  Denying  the  Antecedent;  in  the  second,  the  Fallacy  of 
Affirming  the  Consequent. 

If  a  man  is  a  Christian,  he  forgives; 
J.  S.  is  not  a  Christian; 
.  • .  J.  S.  does  not  forgive. 

If  a  man  is  a  Christian,  he  forgives; 
J.  S.  forgives; 
.  • .  J.  S.  is  a  Christian. 

Turning  from  words  to  things,  the  meaning  of  the  formal 
rule  is  as  follows: 

If  the  presence  of  one  state  of  affairs  (AB)  always  involves 
the  presence  of  another  (CD),  and  if  the  first  state  of  affairs 
(AB)  is  present,  the  second  state  of  affairs  (CD)  must  also  be 
present;  if  the  second  state  of  affairs  (CD)  is  absent,  the  first 
state  of  affairs  (AB)  cannot  be  there  to  involve  its  presence; 
but  the  first  state  of  affairs  (AB)  can  be  absent  without 
involving  the  absence  of  the  second  (CD);  and  the  second 
(CD)  can  be  present  without  involving  the  presence  of  the 
first  (AB). 

These  fallacies  of  '  denying  the  antecedent '  and  '  affirming 
the  consequent  '  would  not  be  fallacies  at  all  if  the  world 
were  so  constituted  that  .there  was  only  one  cause  capable 
of  producing  a  given  effect  or  one  premise  capable  of  involv- 
ing a  given  conclusion.  If  a  person  had  to  be  drowned  in 
order  to  be  killed,  we  could  not  only  say,  '  He  is  drowned, 
therefore  he  is  killed  ',  '  He  is  not  killed,  therefore  he  is  not 
drowned  ' ;  but  we  could  also  say,  '  He  is  not  drowned, 
therefore  he  is  not  killed  ',  and  '  He  is  killed,  therefore  he  is 
drowned  '.  To  avoid  the  fallacy  we  should  think  of  what 
we  are  saying  and  remember  that  the  world  is  not  consti- 
tuted in  this  way,  but  that  any  one  of  several  causes  may  pio- 


1 86  OTHER   DEDUCTIVE   ARGUMENTS. 

duce  essentially  the  same  result  and  any  one  of  several  prem- 
ises involve  the  same  conclusion. 

Disjunctive  Disjunctive  Syllogisms  are  those  which  con- 
syllogisms.  tajn  a  disjunctive  major  premise  and  a  categorical 

minor,  e.g. : 

A  is  either  B  or  C ;        Either  J  is  not  K  or  L  is  M  ; 
A  is  not  B  ;  J  is  K  ; 

.'.  A  is  C.  .  •.    L  is  M. 

In  order  that  any  conclusion  should  be  justified  it  is 
necessary  that  the  minor  premise  deny  the  existence  of  one 
of  the  alternatives  mentioned  in  the  major.  We  cannot  say 
'A  is  either  B  or  C;  it  is  B;  therefore  it  is  not  C'.* 

What  we  must  be  most  careful  about  in  the  case  of  these 
syllogisms  is  to  see  that  the  major  premise  is  really  true; 
that  there  is  no  alternative  which  it  does  not  mention.  We 
should  not  say  'This  man  must  be  either  wise  ,or  foolish,  he 
is  not  wise,  therefore  he  is  foolish' ;  for  there  are  many  per- 
sons of  medium  intelligence  who  cannot  fairly  be  called 
either  wise  or  foolish. 

A  Dilemma  is  'a  syllogism  having  a  hypothetical  major 
premise  with  more  than  one  antecedent  and  a  disjunctive 

minor'.       "  In    common    speech  .  .  .  we  are  said 
Dilemmas.       tQ    ^    jn    a   Dilemma  when    we    have    only    two 

courses  open  to  us  and  both  of  them  are  attended  by 
unpleasant  consequences.  In  arguments  we  are  in  this 
position  when  we  are  shut  into  a  choice  between  two  admis- 
sions and  either  admission  leads  to  a  conclusion  which  we 
do  not  like.  "  t 

According  to  Jevons  the  Dilemma  takes  at  least  three 
different  forms.  "The  first  form  is  called  the  Simple  Con- 
structive Dilemma: 

If  A  is  B,  C  is  D ;    and   if  E  is  F,  C  is  D; 

But  either  A  is  B,    or  E  is  F; 

Therefore  C  is  D. 

*Sec  p.    106  on  meaning  of  '  either'.  -f  Minto,  p.  222. 


DILEMMAS.  187 

"  Thus  '  if  a  science  furnishes  useful  facts,  it  is  worthy  of 
being  cultivated;  and  if  the  study  of  it  exercises  the  reason- 
ing powers,  it  is  worthy  of  being  cultivated;  but  either  a 
science  furnishes  useful  facts,  or  its  study  exercises  the 
reasoning  powers;  therefore  it  is  worthy  of  being  cultivated.' 
'  The  second  form  of  dilemma  is  the  Complex  Constructive 
Dilemma,  which  is  as  follows: 

If  A  is  B,  C  is  D;  and  if  E  is  F,  G  is  H; 
But  either  A  is  B,  or  E  is  F; 
Therefore  either  C  is  D,  or  G  is  H. 

"It  is  called  complex  because  the  conclusion  is  in  the 
disjunctive  form.  As  an  instance  we  may  take  the  argu- 
ment, '  If  a  statesman  who  sees  his  former  opinions  to  be 
wrong  does  not  alter  his  course,  he  is  guilty  of  deceit;  and 
if  he  does  alter  his  course,  he  is  open  to  a  charge  of  incon- 
sistency; but  either  he  does  not  alter  his  course  or  he  does; 
therefore  he  is  either  guilty  of  deceit  or  open  to  a  charge  of 
inconsistency.'  In  this  case  as  in  the  greater  number  of 
dilemmas  the  terms  A,  B,  C,  D,  etc.,  are  not  different." 

The  third  form — the  Destructive  Dilemma — "  is  always  com- 
plex, because  it  could  otherwise  be  resolved  into  two  uncon- 
nected destructive  hypothetical  syllogisms.  It  is  in  the 
following  form : 

If  A  is  B,  C  is  D;  and  if  E  is  F,  G  is  H; 
But  either  C  is  not  D,  or  G  is  not  H  ; 
Therefore  either  A  is  not  B,  or  E  is  not  F. 

"  For  instance,  '  If  this  man  were  wise,  he  would  not  speak 
irreverently  of  Scripture  in  jest;  and  if  he  were  good,  he 
would  not  do  so  in  earnest;  but  he  does  it  either  in  jest  or 
in  earnest;  therefore  he  is  either  not  wise  or  not  good' 
(Whately). 

"  Dilemmatic  arguments  are,  however,  more  often  fal- 
lacious than  not,  because  it  is  seldom  possible  to  find 
instances  where  two  alternatives  exhaust  all  the  possible 


1 88        OTHER  DEDUCTIVE  ARGUMENTS. 

cases,  unless  indeed  one  of  them  be  the  simple  negative  of 
the  other  in  accordance  with  the  law  of  excluded  middle. 
Thus  if  we  were  to  argue  that  '  if  a  pupil  is  fond  of  learning 
he  needs  no  stimulus,  and  that  if  he  dislikes  learning  no 
stimulus  will  be  of  any  avail,  but  that,  as  he  is  either  fond  of 
learning  or  dislikes  it,  a  stimulus  is  either  needless  or  of  no 
avail  ',  we  evidently  assume  improperly  the  disjunctive  minor 
premise.  Fondness  and  dislike  are  not  the  only  two  possi- 
ble alternatives,  for  there  may  be  some  who  are  neither  fond 
of  learning  nor  dislike  it,  and  to  these  a  stimulus  in  the 
shape  of  rewards  may  be  desirable."  * 

Principles  of  logic  have  reference  to  the  relations  of 
objects,  not  to  the  words  in  which  those  relations  are 
expressed.  From  this  it  follows  that  variations 
forms  of  can  be  introduced  into  the  wording  of  an  argu- 
argument?d  ment  without  affecting  its  validity.  One  varia- 
tion that  has  seemed  important  enough  to  be 
discussed  in  almost  every  text-book  since  Aristotle  consists 
in  taking  for  granted  certain  of  the  relations  involved, 
without  any  explicit  mention  of  them.  '  Enthymemes  ', 
'  Epicheiremata  '  and  '  Sorites  '  are  names  for  arguments 
abridged  in  different  ways. 

An  Enthymeme  (from  ev,  in,  and  #J;/YOS",  the  mind)  is  a 
syllogism — usually  categorical — in  which  one  of  the  premises 
or  the  conclusion  is  not  expressed. 

Supposing  the  syllogism  in  question  to  be  this: 

All  men  are  mortal; 
Socrates  is  a  man ; 
Therefore  Socrates  is  mortal ; 

our  reasoning  would  have  been  almost  as  clear  and  more 
effective  rhetorically  if  we  had  merely  said: 

(/)    Socrates  is  a  man, 

Therefore  he  is  mortal  ; 

*  "  Lessons  in  Logic  ",  p.  167. 


THREE  FORMS   OF   ABBREVIATED   ARGUMENT.        189 

or  (2)    All  men  are  mortal, 

Therefore  Socrates  is  mortal; 
or  (j)  All  men  are  mortal, 

And  Socrates  is  a  man.* 

Reasoning  often  takes  the  form  of  a  chain  in  which  the 
conclusion  of  one  syllogism  is  used  as  one  of  the  premises 
of  another,  e.g.  : 

All  A's  are  B's; 
All  B's  are  C's; 
Therefore  all  A's  are  C's. 

All  A's  are  C's; 
All  C's  are  D's; 
Therefore  all  A's  are  D's. 

The  syllogism  which  supplies  such  a  premise  is  called  a 
Prosyllogism ;  that  which  uses  it,  an  Episyllogism. 

When  an  Episyllogism  depends  upon  a  Prosyllogism  which 
is  only  partly  expressed  the  argument  is  called  an  Epichei- 
rema,  e.g. : 

All  A's  are  C's,  for  they  are  B's; 
All  C's  are  D's,  for  they  are  X's; 
Therefore  all  A's  are  D's. 

This  is  "a  double  Epicheirema,  containing  reasons  for 
both  premises  ". 

A  Sorites  is  a  chain  of  prosyllogisms  and  episyllogisms  in 
which  all  the  conclusions  but  the  last  are  unexpressed,  e.g.  : 

All  A's  are  B's;  All  Athenians  are  Greeks; 

All  B's  are  C's;  All  Greeks  are  men; 

All  C's  are  D's;  All  men  are  mortal; 

All  D's  are  E's;  All  mortals  fear; 

Therefore  all  A's  are  E's.  .  • .  All  Athenians  fear. 

*  Where  the  major  premise  is  omitted  the  enthymeme  is  said  to  be  of 
the  first  order  ;  where  the  minor,  of  the  second  ;  where  the  conclusion,  of 
the  third. 


190  OTHER   DEDUCTIVE  ARGUMENTS. 

If  we  put  in  the  suppressed  conclusions,  the  Sorites  is 
resolved  into  these  syllogisms: 

All  A's  are  B's;  All  B's  are  C's;  .  •.  All  A's  are  C's. 

All  A's  are  C's;  All  C's  are  D's;          .  • .  All  A's  are  D's. 
All  A's  are  D's;  All  D's  are  E's;          .  • .  All  A's  are  E's. 

With  reference  to  a  Sorites  it  should  be  observed: 

1)  That    almost    invariably    the   minor  premise   of   each 
syllogism  involved  is  written  first.     A  Sorites  which  begins 
at  the  other  end  seems  jagged. 

2)  That  in  any  valid  Sorites  every  premise  but  the  first 
(i.e.,  the  minor  premise  of  the  first  prosyllogism)  must  be 
universal   and   every  premise  but  the  last  (i.e. ,    the   major 
premise  of  the  last  episyllogism)  affirmative. 

3)  That  while  the  last  syllogism  involved    (the  episyllo- 
gism) may  be  in  any  figure,  each  prosyllogism  must  be  in 
the  first;  and  that  in  the  case  of  each  prosyllogism  it  is  the 
minor  premise  which  the  previous  prosyllogism  supports. 


CHAPTER  XVIII. 
BLUNDERS   IN   WORD   AND   BLUNDERS   IN   THOUGHT. 

FALLACIES  or  blunders  in  reasoning  are  usually  divided 
into  two  great  classes:  '  Logical  '  or  '  Formal  '  (FaUacice.  in 
diclione}  and  '  Non-logical  '  or  '  Material  '  (Fa/tacitf  c.vtra 
diclionem  or  in  re].  When  logic  is  regarded  as  a  science  of 
the  '  forms  of  thought  '  or  the  science  which  treats  of  the 
proper  arrangement  of  words  in  correct  thinking  (on  the 
assumption  that  the  '  forms  '  of  thought  and  the  forms  or 
arrangements  of  words  correspond)  this  distinction  presents 
no  difficulties:  logical  or  formal  fallacies  are  those  which 
result  from  a  violation  of  the  rules  which  logic  lays  down  for 
correct  thinking  and  the  corresponding  arrangement  of 
words;  and  material  or  non-logical  fallacies  are  those  which 
occur  in  spite  of  the  observance  of  these  rules — they  do  not 
depend  upon  the  general  laws  of  thought  or  arrangement  of 
words  at  all,  and  can  only  be  avoided  by  a  knowledge  of  the 
matter  thought  about. 

In  the  foregoing  pages  I  hope  it  has  been  made  plain  that 
the  same  arrangement  or  form  of  words  cannot  be  counted 
upon  to  always  express  the  same  thought.  I  hope  it  has 
been  made  plain  too  that  the  so-called  '  laws  '  and  '  forms  ' 
of  thought  with  which  it  is  often  said  that  logic  deals  have 
no  meaning  whatever  apart  from  the  things  thought  about 
and  the  way  in  which  the  relations  of  these  things  involve 
each  other.  If  these  views  are  correct  it  is  quite  impossible 
to  make  any  fundamental  distinction  between  fallacies  which 

191 


192  BLUNDERS    IN   WORD    AND   IN    THOUGHT. 

are  due  to  some  perversion  of  the  forms  of  thought  and  those 
which  are  due  to  some  mistake  about  the  relations  of  things. 
But  \ve  might  still  distinguish  between  fallacies  which  are 
due  to  some  misconception  about  the  '  matter '  under  dis- 
cussion and  those  which  depend  in  some  way  upon  the 
4  form  '  of  words  used  in  discussing  it.  So  with  the  terms 
*  logical  '  and  '  extra-logical  '.  They  may  be  taken  to  mean 
that  some  fallacies  result  from  a  violation  of  logic  while 
others  do  not.  or  they  may  be  taken  to  mean  that  some  are, 
and  others  are  not,  concerned  with  Jogoi  or  words. 

Now  it  is  true  that  logic  has  not  made  such  elaborate 
provision  against  every  fallacy  possible  as  it  makes  against 
those  already  discussed,  and  yet  fallacious  thinking  is  always 
illogical  and  there  is  no  reason  but  one  of  convenience  why 
books  on  logic  should  discuss  some  and  not  others.  It  is 
not  appropriate  therefore  to  divide  fallacies  into  those  that 
violate  the  rules  of  logic  and  those  that  do  not.  But  there 
is  a  reason  why  we  should  divide  fallacies  into  those  that 
result  in  some  way  from  the  improper  use  of  words  and  those 
that  do  not.  We  may  therefore  accept  this  division  into 
4  logical  '  and  '  extra-logical  '  or  '  material  '  on  the  under- 
standing that  it  is  equivalent  to  a  division  into  blunders  that 
result  mainly  from  the  careless  use  of  words  and  those  that 
<lo  not. 

The  '  logical  '  fallacies  are  usually  subdivided  into  two 
classes  called  '  Purely  logical  ',  "  where  the  fallaciousness 
is  apparent  from  the  mere  form  of  expression  ",  and  '  Semi- 
logical  ',  where  the  fallaciousness  is  not  apparent  from  the 
mere  form  of  expression  but  is  due  to  some  ambiguitv  in  the 
language  used  or  some  misunderstanding  as  to  its  meaning. 
Of  the  '  semi-logical  '  fallacies  we  shall  have  nothing  more 
to  say.  We  have  seen  already  how  insidious  they  are,  why 
they  arise,  and  how  best  to  guard  against  them. 

With  the  '  purely  logical  '  fallacies  we  are  also  familiar. 
They  are  such  blunders  as  we  make  when  we  ignore'  the 
cautions  of  the  syllogism,  or  convert  A  simply  or  O  at  all,  or 


'PURELY    LOGICAL.'  1 93 

reason  that  because  all  S  is  P  all  non-S  is  non-P,  or  infer 
the  falsity  of  a  consequent  from  the  falsity  of 
its  antecedent,  or  the  truth  of  the  antecedent 
from  the  truth  of  the  consequent,  or  the  falsity 
of  a  conclusion  from  the  falsity  of  the  premises,  or  the  truth 
of  the  premises  from  the  truth  of  the  conclusion.  In  all 
such  cases  it  is  '  apparent  from  the  mere  form  of  expres- 
sion '  that  the  reasoning  is  inconclusive;  the  blunder  can 
be  detected  without  inquiring  into  the  truth  of  the  premises 
or  even  into  the  meaning  of  the  terms;  so  that  a  purely 
logical  fallacy,  unlike  any  of  the  others,  can  be  detected 
when  the  terms  are  mere  unmeaning  words  or  symbols  such 
as  S,  M  and  P,  or  X,  Y  and  Z. 

The  strange  thing  about  these  so-called  purely  logical 
fallacies  is  that  they  are  committed  so  often.  How  is  it 
possible,  we  may  ask,  to  think  so  badly  ?  If  the  reader  will 
ask  the  following  questions  to  some  unsuspecting  person  and 
does  not  allow  very  much  time  to  elapse  between  the 
answering  of  one  and  the  asking  of  the  next,  the  result  of 
the  experiment  may  help  to  make  the  matter  clear: 

Who  was  the  first  man  ? 

Who  \vas  the  first  woman  ? 

Who  killed  Cain  ? 

Abel  did  not  kill  Cain,  but  his  name  will  usually  be  men- 
tioned, or  at  ka?t  come  to  mind,  merely  because  it  comes 
naturally  at  the  end  of  the  series  '  Adam,  Eve,  Cain  '  and 
fits  into  the  atmosphere  of  murder.  It  is  largely  a  mere 
matter  of  the  verbal  jingle,  the  answer  resulting  from  the 
same  law  of  habit  in  the  nervous  system  that  accounts  for 
putting  one's  pen  in  the  paste-pot  after  using  the  brush. 
Most  of  these  so-called  purely  logical  fallacies  come  in  pre- 
cisely the  same  way.  Inference  is  in  the  air  and  the  jingle 
seems  to  fit,  so  we  spurt  out  something  when  the  premises 
will  not  justify  any  inference  whatever,  or  an  '  All  '  or  a 
'  No  '  that  fits  the  jingle  when  the  premises  justify  only  a 
'  Some  '.  If  we  sav: 


I94  BLUNDERS   IN   WORD   AND   IN   THOUGHT. 

All  Xis  Y; 
All  Y  isZ; 
.  • .  All  X  is  Z, 
the  reasoning  is  valid,  but  if  we  say: 

No  X  is  Y;  i         or  No  X  is  Y; 

No  Y  isZ;   C  All  Y  is  Z; 

.  • .  No  X  is  Z ;   )  .  • .  No  X  is  Z, 

it  is  not  valid  though  we  have  merely  substituted  '  No  '  for 
'  All  '  or  '  No  X  '  for  '  All  X '  throughout,  without  affecting 
the  jingle.  Indeed  if  we  had  only  said  '  No-X '  instead  of 
'No  X'  the  reasoning  in  the  last  case  would  have  been 
precisely  similar  to  that  in  the  first  and  just  as  valid.  Again 
if  we  say 

Five  francs  are  a  dollar; 
Four  shillings  are  a  dollar; 
.  • .  Five  francs  are  four  shillings, 

the  inference  is  perfectly  valid;  but  if  we  say  in  precisely 
similar  form 

Blades  of  grass  are  green; 
Frogs  are  green ; 
.  • .  Blades  of  grass  are  frogs, 

the  inference  is  not  valid.  The  reason  is,  of  coarse,  that 
the  copuhi  '  are  '  is  used  in  different  senses  in  the  two 
arguments;  but  when  we  do  not  stop  to  think  of  the  sense, 
the  familiar  jingle,  assisted  perhaps  in  this  case  by  some 
recollection  of  Euclid's  axiom  that  '  things  equal  to  the  same 
thing  are  equal  to  each  other',  lures  us  on  to  danger. 

hi  spite  of  a  real  confusion  of  meaning  sometimes  asso- 
ciated \vith  some  of  these  '  purely  logical  fallacies  ',  they  can 
hardly  be  called  the  result  of  bad  thinking;  because  they  are 
m  >t  t lie  result  of  thinking  at  all,  but  only  of  a  rellex  act. 
On  this  account  it  might  have  been  more  appropriate  to  call 
them  the  Reilex  Fallacies  or  the  Jingle  Fallacies.  . 

As   there  are  two  classes  of  verbal   fallacies,  so  also  there 


TWO   KINDS   OF   MATERIAL   FALLACIES.  195 

arc  two  classes  of  the  material  or  non-verbal  fallacies,  which 

may  be  called  respectively  Fallacies  of  the  For- 

,    Two  kinds 

gotten  Issue  and   rallacies   of  the   Ill-conceived    of  material 
TT    •  T-  11      •          c     i       T-  fallacies. 

Universe,      rallacies  of  the  rorgotten  Issue  are 

not  particularly  characteristic  of  deduction;  but  some  of 
them  are  usually  discussed  in  connection  with  it,  and  there- 
fore we  shall  speak  of  them  in  the  next  chapter.  In  the 
chapter  after  that  we  shall  discuss  Fallacies  of  the  Ill-con- 
ceived Universe.  These  do  not.  belong  to  the  traditional 
field  of  deduction,  because  there  are  no  rules  for  verbal 
manipulation  which  they  break.  Yet  I  have  tried  to  show 
that  all  deductive  inference  depends  upon  the  assumption 
that  things  have  certain  general  relations,  and  that  deductive 
fallacies  occur  when  these  relations  are  overlooked;  and  if 
this  is  correct  these  fallacies  of  the  Ill-conceived  Universe 
are  essentially  similar  to  the  fallacies  of  deduction  in  their 
ultimate  nature,  though  they  may  not  be  caused  like  them 
by  a  verbal  jingle. 

Nothing  has  been  said  in  the  foregoing  pages  about  the 
fallacy  known  as  '  Non  Sequitur'.  This  name  is  really 
applicable,  as  the  words  imply,  to  every  argument 
in  which  the  conclusion  does  not  follow,  and  in  Sequitur. 
this  sense  of  the  words  every  fallacy  is  a  Non  Sequitur. 
But  the  phrase  is  often  applied  in  a  more  restricted  sense  to 
those  arguments  onlv  in  which  the  conclusion  does  not  even 
appear  to  follow,  except  perhaps  to  the  most  hasty  and 
careless  of  reasoncrs;  as  in  the  following  examples:  The 
earth  is  round;  therefore  there  is  no  atmosphere  on  the 
moon.  "  Every  one  desires  happiness,  and  virtuous  people 
arc  happy,  therefore  every  one  desires  to  be  virtuous.'' 
"  Episcopacy  is  of  Scripture  origin,  the  Church  of  England 
is  the  only  established  church  in  England;  ergo  the  church 
established  is  the  church  that  should  be  supported."  The 
subject  requires  iu  further  consideration. 


CHAPTER   XIX. 
THE  FORGOTTEN   ISSUE. 

A  FALLACY  of  the  Forgotten  Issue  is  committed  when  we 
forget  what  it  was  that  an  argument  was  intended  to  prove, 
and  either  take  that  very  thing  or  something  equivalent  to  it 
and  quite  as  doubtful  for  granted,  or  else  prove  something 
which  is  not  equivalent  to  the  point  at  issue  and  then  assume 
that  we  have  proved  the  point  itself.  In  the  first  case  the 
fallacy  is  called  Petitio  Principii  or  Begging  the  Question. 
In  the  second  it  is  called  Ignoratio  Elenchi  or  a  fallacy  of 
Irrelevance.  Fach  of  these  two  fallacies  of  the  forgotten 
issue  takes  several  forms. 

The  fallacy  of  Petitio  Principii  is  nut  committed  unless 
there  is  a  show  of  proof.  Nobody  commits  it  who  merely 
pnitio  sa)s  '  I  assume  these  conclusions  to  be  true,  and 

Principii.  j  c]o  no(-  try  to  prove  them'.  But  a  person  does 
commit  it  if  he  thinks  he  is  proving  his  conclusions  when 
he  is  really  assuming  them,  or  is  assuming  a  premise  that  is 
not  admitted  or  would  not  be  admitted  if  its  real  significance 
were  understood.  Often  the  premise  is  actually  proved  from 
the  conclusion,  or  '  is  such  as  would  naturally  and  properlv 
be  so  proved  '.  But  in  any  case  in  which  the  fallacy  is 
present  the  conclusion  seems  to  be  more  fully  proved  by  the 
argument  than  it  really  is,  because  it  is  not  clearly  understood 
how  nearly  equivalent  is  that  which  is  taken  f;>r  granted  to 
that  which  is  to  be  proved;  e.g.,  "Whoever  refuses  to 
believe  in  the  inspiration  of  the.  Bible  makes  the  Most  High 

iq6 


PETITIO   PRINCIPII.  197 

a  deceiver;  for  has  he  not  told  us  that  '  All  scripture  is  given 
by  inspiration  of  God  '  ?  "  Of  course  we  have  no  reason  to 
believe  that  it  was  really  God  who  said  that  all  scripture  is 
given  by  his  inspiration  unless  we  already  assume  that  the 
Bible  or  some  part  of  it  is  inspired. 

Whately  directs  attention  to  the  fact  that  the  English 
language  is  peculiarly  "  suitable  for  the  fallacy  of  Pttitio 
Principii,  from  its  being  formed  from  two  distinct  languages, 
and  thus  abounding  in  synonymous  expressions  which  have 
no  resemblance  in  sound,  and  no  connection  in  etymology; 
so  that  a  Sophist  may  bring  forth  a  proposition  expressed  in 
words  of  Saxon  origin,  and  give  as  a  reason  for  it  the  very 
same  proposition  stated  in  words  of  Norman  origin;  e.g. , 
1  To  allow  every  man  an  unbounded  freedom  of  speech  must 
always  be,  on  the  whole,  advantageous  to  the  State;  for  it 
is  highly  conducive  to  the  interests  of  the  community,  that 
each  individual  should  enjoy  a  liberty  perfectly  unlimited 
of  expressing  his  sentiments  '  ". 

A  blunder  of  this  same  sort  is  committed  when  a  student 
says  that  two  chemicals  are  sure  to  unite  since  they  have  an 
affinity  for  each  other;  or  that  he  knows  unsupported  objects 
will  fall  to  the  earth  from  the  fact  that  they  are  attracted 
towards  it. 

"  Connected    with    this    fallacy  is    the   rhetorical    device 
[already    discussed]     of    Question-begging   Epithets.       Thus, 
though  the  matter  we  are  discussing  is  open  to  dispute,  we 
may  speak  of  a  nefarious  project,  a  laudable  am-   includes 
bition,   an  astute  act,   a  far-sighted  policy,  and   ePithets- 
so  on,  attempting,  by  means  of  a  carefully  selected  epithet, 
to  assume  the  point  at  issue,  or  at  least  to  create  an  unfair 
prejudice  in  the  mind  of  the  hearer  or  reader  whom  we  ad- 
dress. "  * 

When  a  conclusion  is  based  upon  a  premise  which  in  an 
earlier  stage   of   the   argument  was  itself  based 
upon  this  very  conclusion,  the  reasoning  is  said 

*  Fowler's  "  Deductive  Logic  "  (Clarendon  Press). 


198  THE   FORGOTTEN  ISSUE. 

to  be  in  a  Circle   (Circulus  in   Probando).      Here  are  some 
examples  : 

First  Syllogism.  Second  Syllogism. 

A  is  B;  A  is  C; 

B  is  C;  C  is  B; 

.  • .  A  is  C.  .  • .  A  is  B. 

"  Some  mechanicians  attempt  to  prove  (what  they  ought 
to  lay  down  as  a  probable  but  doubtful  hypothesis)  that 
every  particle  of  matter  gravitates  equally;  '  why  ?  '  because 
those  bodies  which  contain  more  particles  ever  gravitate 
more  strongly,  i.e.,  are  heavier:  '  but  (it  may  be  urged)  those 
which  are  heaviest  are  not  always  more  bulky;  '  '  no,  but 
still  they  contain  more  particles,  though  more  closely  con- 
densed ; '  '  how  do  you  know  that  ?  '  '  because  they  are 
heavier;  '  '  how  does  that  prove  it  ?  '  '  because  all  particles 
of  matter  gravitating  equally,  that  mass  which  is  specifically 
the  heavier  must  needs  have  the  more  of  them  in  the  same 
space'"  (Whately).  'Any  man  who  would  marry  such  a 
woman  must  have  something  wrong  with  him.'  'Why, 
what  is  the  matter  with  his  wife  ?  '  'It  is  matter  enough  to 
be  willing  to  marry  such  a  man  as  he  is.' 

If  there  are  a  large  number  of  intermediate  steps  and  the 
argument  is  a  long  one  it  may  be  very  difficult  to  detect  the 
circle.  This  fallacy,  like  a  good  many  others,  can  be  best 
guarded  against  by  making  the  shortest  and  simplest  possible 
summary  of  any  argument  that  claims  our  interest. 

Ignoratio  Elenchi  or  Irrelevance,  the  other  fallacy  of  the 
forgotten  issue,  consists  merely  in  arguing  beside  the  point. 
"  I  am  required  by  the  circumstances  of  the  case  (no  matter 
I  ratio  why)  to  prove  a  certain  conclusion;  I  prove, 
EiencM.  no(.  that,  but  one  which  is  likely  to  be  mistaken 
for  it; — in  this  lies  the  fallacy.  .  .  .  For  instance,  in- 
stead of  proving  that  '  this  prisoner  lias  committed  an 
atrocious  fraud  ',  you  prove  that  '  the  fraud  he  is  accused  of 
is  atrocious  ' ;  instead  of  proving,  as  in  the  well-known  tale 
of  Cyrus  and  the  two  coats,  that  '  the  taller  boy  had  a  right 


IGNORATIO    ELENCHI.  199 

to  force  the  other  boy  to  exchange  coats  with  him  ',  you 
prove  that  '  the  exchange  would  have  been  advantageous  to 
both  ' ;  instead  of  proving  that  '  a  man  has  not  a  right  to 
educate  his  children  or  dispose  of  his  property  in  the  way  he 
thinks  best ',  you  show  that  '  the  way  in  which  he  educates  his 
children  or  disposes  of  his  property  is  not  really  the  best' ; 
instead  of  proving  that  '  the  poor  ought  to  be  relieved  in  this 
way  ',  you  prove  that  '  they  ought  to  be  relieved' .  ...  A 
good  instance  of  the  employment  and  exposure  of  this  fallacy 
occurs  in  Thucydides,  in  the  speeches  of  Cleon  and  Diodotus 
concerning  the  Mitylenaeans:  the  former  (over  and  above  his 
appeal  to  the  angry  passions  of  his  audience)  urges  the  justice 
of  putting  the  revolters  to  death;  which,  as  the  latter 
remarked,  -was  nothing  to  the  purpose,  since  the  Athenians 
were  not  sitting  vs\  judgment,  but  in  deliberation,  of  which  the 
proper  end  is  expediency. ' '  * 

It  is  interesting  to  find  counterparts  of  this  story  in  the 
history  of  our  own  times.  The  following  sentences  from 
Bismarck's  Autobiography  (Chapter  XX)  refer  to  the  Austrian 
proposals  for  peace  after  the  Prussian  victories  in  the  war  of 
1866: 

"  I  unfolded  to  the  King  [of  Prussia]  the  political  and 
military  reasons  which  opposed  the  continuation  of  the  war. 

"  We  had  to  avoid  wounding  Austria  too  severely;  we  had 
to  avoid  leaving  behind  in  her  any  unnecessary  bitterness  of 
feeling  or  desire  for  revenge;  we  ought  rather  to  reserve  the 
possibility  of  becoming  friends  again  with  our  adversary  of 
the  moment,  and  in  any  case  to  regard  the  Austrian  state  as 
a  piece  on  the  European  chess-board  and  the  renewal  of 
friendly  relations  with  her  as  a  move  open  to  us.  If  Austria 
were  severely  injured,  she  would  become  the  ally  of  France 
and  of  every  other  opponent  of  ours;  she  would  even  sacrifice 
her  anti-Russian  interests  for  the  sake  of  revenge  on 
Prussia.  .  .  . 

*  Whately,  "  Elements  of  Logic  ",  third  edition,  London,  1829. 


200  THE   FORGOTTEN   ISSUE. 

"  To  all  this  the  King  raised  no  objection,  but  declared 
the  actual  terms  as  inadequate,  without,  however,  definitely 
formulating  his  own  demands.  Only  so  much  was  clear, 
that  his  claims  had  grown  considerably  since  July  4.  He 
said  that  the  chief  culprit  [Austria]  should  not  be  allowed 
to  escape  unpunished,  and  that  justice  once  satisfied,  we 
could  let  the  misled  backsliders  [the  smaller  German  states 
that  had  sided  with  Austria]  off  more  easily,  and  he  insisted 
on  the  cessions  of  territory  from  Austria  which  I  have  already 
mentioned.  I  replied  that  we  were  not  there  to  sit  in  judg- 
ment, but  to  pursue  the  German  policy.  Austria's  conflict 
in  rivalry  with  us  was  no  more  culpable  than  ours  with  her; 
our  task  was  the  establishment  or  initiation  of  a  German  national 
unity  under  the  leadership  of  the  King  of  Prussia. 

"  Passing  on  to  German  states,  he  spoke  of  various 
acquisitions  by  cutting  down  the  territories  of  our  opponents. 
I  repeated  that  we  were  not  there  to  administer  retributive 
justice,  but  to  pursue  a  policy;  that  I  wished  to  avoid  in 
the  German  federation  of  the  future  the  sight  of  mutilated 
territories,  whose  princes  and  peoples  might  very  easily 
(such  is  human  weakness)  retain  a  lively  wish  to  recover 
their  former  possessions  by  means  of  foreign  help;  such  allies 
would  be  very  unreliable."  * 

"  So  Canning,  in  a  speech  in  the  House  of  Commons  in 
reply  to  Mr.  Percival,  says:  '  The  question  is  not,  as  assumed 
by  my  opponent,  whether  we  shall  continue  the  war  in  the 
Peninsula,  but  whether  it  is  essential  to  our  success  in  the 
war  that  our  present  system  of  currency  remain  unchanged. ' 
Thus  it  is  not  unusual,  after  a  protracted  debate,  for  the 
cooler  thinkers  to  preface  their  remarks  with  reminding  the 
audience  of  the  real  nature  of  the  point  on  which  issue  is 
joined;  and  the  longer  and  more  heated  the  discussion,  the 
greater  the  need  for  these  monitory  exordiums.  For, 
especially  when  the  field  of  debate  is  large,  the  combatants 

*   "  Bismarck  the  Man  and  the  Statesman".     (Harper  &  Bros.,  1891).) 


INCLUDES    'AD   HOMINEM '  2OI 

often  join  issue  on  the  wrong  points,  or  do  not  join  issue  at 
all.  One  goes  to  the  east,  another  to  the  west;  one  loses 
the  proposition  in  question,  and  wanders  amidst  a  crowd  of 
irrelevant  details;  another  mistakes  contraries  for  contradic- 
tories, or  universals  for  particulars;  and,  after  some  hours  of 
storm,  they  know  not  what  they  have  been  discussing.  One 
has  made  out  a  case  which  his  adversary  admits,  the  more 
readily  as  it  has  not  the  least  bearing  on  the  question; 
another,  having  overthrown  a  similar  collateral  proposition, 
makes  his  pretended  triumph  resound  over  the  field;  yet 
another,  having  been  rather  shattered  by  reasons,  appeals  to 
the  prejudices  of  his  auditory,  and,  overwhelming  his  more 
rational  antagonist  with  ridicule  and  abuse,  comes  off  the 
apparent  and  acknowledged  victor  in  the  contest."  * 

There  are  many  subjects  that  have  to  be  discussed  at 
some  length  before  it  is  possible  to  tell  precisely  what  the 
point  or  points  at  issue  are;  but  whenever  there  is  a  definite 
issue  we  should  try  very  hard  in  our  discussions  and  in  our 
private  thinking  to  stick  to  it.  In  our  courts  of  law  the  rule 
that  all  testimony  must  be  relevant  is  enforced  very  strictly. 
Unfortunately  the  corresponding  rule  about  parliamentary 
discussions  cannot  be  enforced  so  strictly. 

Two  special  forms  of  Ignoratio  Elenchi  are  called  the 
Argumentum  ad  Hominem  and  the  Argumentum  ad  Popu- 
lum.  These  terms  are  applied  in  a  rather  loose  inciuaes  'ad 
sense  to  any  argument  that  appeals  to  feeling  or  tcminem'. 
that  depends,  not  on  the  real  question  at  issue,  but  upon 
the  personality  of  any  of  the  parties  involved,  including 
the  hearers.  As  mere  appeals  to  the  desires  or  passions  of 
one's  hearers  these  arguments  have  been  discussed  already. 
As  involving  confusion  between  the  real  issue  and  some  false 
issue  they  have  not.  As  a  form  of  Ignoratio  Elenchi  the 
Argumentum  ad  Hominem  often  consists  in  supposing  that 
\ve  have  won  our  case  because  we  have  succeeded  in  em- 

*  Davis,  "Theory  of  Thought",  pp.  277-8.     (Harpers,  no  date.) 


2C2  THE   FORGOTTEN   ISSUE. 

barrassing  an  opponent  by  some  personal  reference  that 
has  really  nothing  to  do  with  it.  If  I  am  accused  of  ex- 
travagance I  do  not  answer  the  accusation  though  I  may 
silence  the  accuser  by  proving  that  he  himself  is  no  better; 
if  my  opinions  are  attacked  I  cannot  substantiate  them  by 
replying  that  my  opponent  once  held  them  himself.  Such 
a  retort  I  may  have  a  perfect  right  to  make,  but  I  have  no 
right  to  confuse  it  with  a  vindication  of  my  own  position. 

Undoubtedly  it  was  the  great  danger  of  confusing  issues 
when  questions  of  personality  are  once  introduced  that  made 
our  common  law  exclude  as  irrelevant  all  evidence  as  to  the 
general  character  of  the  parties  concerned  even  in  cases  in 
which  such  evidence  might  seem  to  the  layman  very  relevant 
indeed.  The  courts  try  to  decide  each  particular  case  on  its 
individual  merits,  and  not  to  give  any  man  a  favorable  or 
unfavorable  verdict  merely  because  his  general  character  is 
good  or  bad;  they  know  that  in  many  individual  cases  good 
men  are  in  the  wrong  and  bad  men  in  the  right;  and  they 
know  enough  about  human  nature  to  realize  that  if  questions 
of  general  character  are  dwelt  upon  the  jury  will  be 
influenced  by  them  far  more  than  they  should  be  in  order  to 
decide  the  real  question  at  issue  on  its  merit?. 

The  Argumentum  ad  Populum  is  practically  indistinguish- 
able from  the  Argumenlum  ad  Honnncm.  It  is  defined  as 
"an  appeal  to  the  pas.-ions,  prejudices,  etc.,  of  the  multi- 
tude". '  The  fallacy  usually  occurs  in  the  course  of  long 
harangues,  where  the  multitude  of  words  and  figures  leaves 
room  for  cunfu>ion  of  thought  and  forget ful ness. "  Here 
lies  the  danger  of  brilliant  oratory  and  startling  metaphors. 
\\hatever  one  may  believe  to-day  about  the  comparative 
values  of  a  single  and  a  double  monetary  standard  of  value, 
and  the  wisdom  of  suddenly  changing  from  one  to  the 
other,  it  is  certainly  startling  to  think  how  half  the  country 
was  swept  away,  in  the  spring  of  1896,  and  a  difficult 
economic  problem  fur  a  time  apparently  settled,  by  a  dazzling 
though  empty  metaphor  about  thrusting  a  crown  of  thorns 


INCLUDES    'AD   HOMINEM'.  203 

upon  the  brow  of  labor  and  crucifying  mankind  upon  a  cross 
of  gold.  The  real  question  at  issue  was,  not  whether  labor- 
ing men  should  or  should  not  be  unjustly  treated  and  man- 
kind in  general  oppressed,  but  whether  a  given  policy  would 
tend  in  the  long  run  to  diminish  injustice  and  oppression, 
or  to  increase  it. 


CHAPTER  XX. 
THE   ILL  CONCEIVED   UNIVERSE. 

LOGIC  deals,  as  we  have  seen,  with  the  mutual  implica- 
tions of  relations.  If  the  object  A  possesses  the  permanent 
quality  B  and  the  object  C  does  not,  we  know 
assumed  that  A  and  C  are  not  identical.  Thus  the  pres- 
ence of  a  certain  relation  of  subject  and  attribute 
in  one  case  and  its  absence  in  another  proves  the  absence  of 
a  certain  relation  -of  individual  identity.  These  are  the  rela- 
tions concerned,  but  we  can  reason  as  we  do  about  them 
only  because  we  already  know  or  assume  that  there  are  such 
things  as  separate  individual  objects,  that  these  objects  can 
have  qualities,  that  qualities  can  be  more  or  less  permanent, 
that  we  are  capable  of  recognizing  the  difference  between 
qualities  that  are  permanent  and  those  that  are  not,  and  so 
on.  These  assumptions  and  probably  a  great  many  more 
form  a  sort  of  background  for  the  reasoning  in  question. 
They  constitute  as  it  were  the  universe  in  which  the  relations 
specified  in  the  syllogism  exist,  a  universe  without  which 
they  would  lose  entirely  the  significance  which  they  now 
possess.  It  is  a  universe  which  human  beings  naturally  take 
for  granted;  but  if  in  the  world  to  come  we  should  discover 
that  there  are  really  no  such  things  as  separate  individual 
objects  and  no  such  relations  as  those  of  subject  and  attri- 
bute, then  we  should  be  compelled  to  revise  all  our  rules  of 
logic  and  reason  in  some  other  way.  A  simple  syllogism 
which  seems  to  us  now  to  be  perfectly  valid  would  then  be 

204 


THE   ASSUMED   UNIVERSE.  205 

seen  to  be  absolutely  inconclusive.  Indeed  it  would  seem 
so  inconsequent  as  to  be  utterly  incomprehensible  unless  we 
could  remember  our  old  earthly  point  of  view — the  universe 
in  which  we  reasoned — and  judge  the  argument  from  that 
standpoint.  We  could  then  say  :  '  Assuming  the  fundamental 
relations  of  things  to  be  thus  and  thus,  the  reasoning  is 
perfectly  valid;  but  then  these  are  not  the  actual  relations; 
the  blunder  rested  upon  a  wrong  conception  of  the  back- 
ground or  universe,  and  it  could  not  be  corrected  until  that 
conception  was  outgrown  '. 

In  this  example  the  relations  which  I  have  supposed  to 
be  improperly  assumed  are  amongst  the  most  fundamental 
relations  of  all  reality.  That  is  why  the  falsity  of  the 
assumption  would  involve  the  worthlessness  of  all  our  rules 
of  formal  logic.  The  universe  of  discourse  included  only 
relations  common  to  the  whole  of  the  actual  universe.  Of 
course  we  human  beings  never  in  this  life  can  test  these  most 
fundamental  assumptions  of  all,  and  I  suppose  them  to  be 
questioned  only  for  the  sake  of  illustration.  But  as  a  matter 
of  fact  most  of  our  reasoning  is  about  matters  in  some 
special  universe,  where  not  only  these  but  a  great  many 
other  relations  are  taken  for  granted.  That  is  why  it  is  so 
difficult  for  any  one  but  an  expert  in  that  particular  field  to 
criticise  the  logic  in  any  scientific  or  other  technical  argu- 
ment. In  even  a  game  of  whist,  for  example,  it  would  not 
be  possible  to  infer  anything  about  your  opponent's  hand 
unless  you  knew  the  rules  of  the  game,  and  even  then  the 
very  perfection  of  your  reasoning  might  lead  you  astray  if 
you  supposed  he  was  playing  the  long  game  when  as  a  matter 
of  fact  he  was  playing  the  short.  So  one  might  solve  no 
end  of  chess  problems  with  great  ingenuity,  yet  get  them  all 
wrong,  if  he  supposed  that  pawns  always  moved  straight 
forward,  that  a  queen  could  move  like  a  knight,  or  that  all 
the  chessmen  moved  like  checkers. 

A  more  serious  example  of  the  sort  of  thing  I  have  in 
mind  is  found  in  Plato's  "  Phaedo  ".  Many  students  who 


206  THE   ILL.CONCE1VED   UNIVERSE. 

read  Socrates'  argument  for  the  immortality  of  the  soul,  there 
given,  say  that  where  the  parties  to  the  dialogue  seemed  to 
find  the  argument  more  or  less  conclusive,  they  can  find  no 
argument  at  all ;  or  at  least  no  connection  between  the 
premises  and  the  alleged  conclusions.  The  trouble  is  that 
they  do  not  realize  the  conceptions  of  life  which  Socrates  and 
his  friends  accepted  as  a  matter  of  course.  Throughout  the 
dialogue  it  is  assumed,  for  instance,  that  every  living  thing, 
whether  animal  or  plant,  must  have  a  soul  to  give  it  life — to 
animate  it.  If  to  this  is  added  the  further  assumption  that 
new  souls  are  not  created,  does  it  not  follow  that  life  would 
have  ceased  to  exist  ages  ago  unless  the  soul  which  animated 
one  individual  were  reincarnated  after  the  death  of  that  indi- 
vidual in  some  other,  and  so  in  in  scecula  sceculorum  f  Thus 
by  getting  back  into  Plato's  universe — into  the  conceptions 
which  serve  as  a  background  of  the  argument — we  find  sense 
where  otherwise  we  find  only  nonsense;  and  if  his  argument 
seems  to  us  inconclusive  it  is  only  because  his  universe 
seems  unreal. 

Another  instance  of  the  same  kind  is  found  in  the  con- 
troversy between  Locke  and  Leibnitz  about  innate  ideas. 
Locke  said  it  was  absurd  to  suppose  that  the  mind  contained 
a  set  of  ideas  ready-made  from  birth,  though  we  had  no 
conscious  knowledge  of  some  of  them  until  a  great  many 
years  afterwards.  Leibnitz  replied  that  it  was  much  more 
absurd  to  suppose  that  such  ideas  as  those  of  right  and  wrong 
or  of  cause  and  effect  could  be  conveyed  into  the  mind 
through  any  one  or  all  of  the  five  senses.  And  so  the  dis- 
cussion proceeded,  the  adherents  of  each  champion  seeing 
the  absurdities  of  the  other.  The  conflict  was  necessarily 
interminable  until  in  a  later  age  it  was  realized  that  the 
advocates  of  both  views  assumed  the  same  false  universe,  for 
everybody  assumed  that  in  some  way  or  other  the  mind 
contains  a  kind  of  things  called  ideas  which  must  have  got 
there  in  some  way  or  other.  But  it  is  really  just  as  absurd 
to  ask  how  the  mind  comes  to  contain  its  various  ideas  as 


THE   ASSUMED   UNIVERSE.  207 

to  ask  now  a  frog  comes  to  contain  its  various  jumps.  A 
frog  does  not  contain  things  called  jumps;  it  merely  acts  in 
a  way  we  call  jumping;  and  the  mind  does  not  contain 
things  called  ideas;  it  thinks. 

So  again  with  the  deistic  controversy  about  the  possibility 
of  miracles.  Both  sides  took  it  for  granted  that  the  world 
had  been  wound  up  and  started  like  a  clock;  but  the  deists 
said  that  God  the  clockmaker  never  intervened  by  a  miracle 
to  disturb  its  running,  while  the  orthodox  said  he  did.  The 
question  was  one  of  intervention  or  non-intervention;  and 
it  did  not  occur  to  either  side  that  nature  was  after  all  nothing 
but  a  visible  and  tangible  aspect  of  God,  not  something  sepa- 
rate with  which  perhaps  he  might  not  be  able  to  interfere. 

And  so  it  goes  through  the  whole  history  of  philosophy. 
Each  age  is  dominated  by  some  particular  conception  of  the 
general  constitution  of  things;  and  in  that  age  the  mutual 
relations  of  any  particular  facts  are  necessarily  conceived  with 
reference  to  the  assumed  nature  of  the  whole  of  which  they 
are  parts — of  the  background  from  which  they  stand  out — 
of  the  frame  into  which  they  must  fit.  In  the  next  age  there 
is  a  new  conception  of  the  background— a  new  metaphor, 
perhaps,  to  express  the  deepest  relations  of  things,  — and  the 
reasoning  that  before  had  seemed  absolutely  demonstrative 
now  seems  almost  childish. 

In  the  cases  just  mentioned  the  assumption  of  the  universe 
in  question  was  unconscious  and  practically  inevitable. 
The  same  assumption  of  a  universe  is  made  consciously  in 
the  old  Fallacy  of  Many  Questions,  e.g  :  '  Have  you  cast 
your  horns  ?  '  '  Have  you  left  off  beating  your  father  ?  '  'Is 
the  king  of  Eutopia  dead  ?  '  '  \Yhy  did  you  take  my  purse  ?  ' 
'  Have  you  got  over  your  fit  of  temper  ?  '  etc.  Here  of 
course  the  assumption  is  that  you  have  had  horns, that  there 
is  a  king  of  Eutopia,  etc.,  and  it  is  impossible  to  answer 
either  '  Yes  '  or  '  No  '  to  the  question  without  seeming  to 
admit  the  assumption.* 

*  Sometimes  the  Fallacy  of  Many  Questions  is  committed  to  the  em- 


2o8  THE  ILL-CONCEIVED   UNIVERSE. 

A  Confusion  of  Universes  occurs  when  we  introduce  into 

any  universe  something  which  cannot  possibly  be  subject  to 

the  relations  by  which  that    universe    is  distin- 

Thft 

confusion  of  guished,  or  when  we  introduce  some  other  rela- 
tion which  is  inconsistent  with  them.  All  kinds 
of  absurd  questions  rest  upon  such  confusion.  If  you  ask 
whether  this  triangle  has  eaten  its  dinner,  I  can  hardly  say 
even  '  No  '  without  seeming  to  admit  your  absurd  assumption 
that  a  triangle  is  the  kind  of  thing  that  eats  a  dinner.  Here 
of  course  there  is  an  improperly  assumed  universe;  but  the 
assumption  involves  a  more  or  less  obvious  incongruity.  In 
his  book  on  "  The  Nervous  System  and  the  Mind  "  *  Charles 
Mercier  points  out  with  admirable  clearness  a  somewhat 
less  obvious  incongruity  of  the  same  sort. 

"  It  is  not  to  be  denied  that  there  is  a  large  amount  of 
writing  about  the  mind,  and  about  the  connection  of  the 
mind  with  the  body,  which  is,  strictly  speaking,  nonsense. 
.  .  .  Such  propositions  are  neither  correct  nor  erroneous — 
neither  true  nor  false.  They  are  nonsense.  .  .  .  Take  an 
instance.  Try  to  think  of  a  feeling  passing  along  a  nerve. 
We  often  speak  familiarly  of  a  toothache  shooting  along  a 
nerve;  is  this  an  accurate  expression  ?  Take  the  nerve. 
Dissect  it  out.  Lay  it  on  the  table  before  you.  It  is  a  gray 
thread,  four  inches  long,  made  up  of  fibres  bound  together. 
Now  take  a  toothache  and  set  it  running  along  the  nerve. 
You  cannot.  Why  ?  It  ran  along  the  nerve,  you  said, 
when  it  was  in  the  body;  why  cannot  it  do  so  now? 
Because,  you  will  say,  the  nerve  is  no  longer  connected  with 

barrassment  of  the  questioner  instead  of  the  person  questioned.  Many  of 
the  typical  Irish  jokes  belong  to  this  class,  such  for  example  as  the  story 
of  the  Irishman  who  was  being  tried  for  assaulting  a  Chinaman  in  front 
of  the  Palmer  House  and  had  arranged  with  a  friend  to  prove  an  alibi. 
He  conducted  his  own  defence  and  when  the  time  came  to  question  the 
•witness  he  put  in  some  preliminary  flourishes  and  continued  :  'Then, 
Patrick  Murphy,  on  your  oath,  sir,  where  was  I  when  I  struck  the 
Chinaman  in  front  of  the  Palmer  House  ? ' 
*  Macmillan,  1 888. 


THE  CONFUSION   OF   UNIVERSES.  209 

the  brain.  Take  another  nerve,  then,  and  do  not  separate 
it  from  the  body;  but  pinch  it,  cut  it,  burn  it,  or  galvanize 
it.  What  torture!  what  excruciating  agony!  Surely  this 
pain  is  in  the  nerve;  you  feel  it  there.  Wait  a  little;  let  us 
consider.  The  nerve  is  made  up  of  axis-cylinders  and 
padding;  in  which  is  the  pain  ?  Certainly  not  in  the 
padding;  it  must  then  be  in  the  axis-cylinders.  The  axis- 
cylinders  are  gray  threads  of  protein  substance,  which  is 
made  up,  like  all  other  matter,  of  molecules  swinging  in 
space.  Now,  where  is  the  pain  ?  Is  it  in  the  molecules  or 
in  the  intervening  space  ?  And  how  does  it  pass  along  the 
nerve  ?  Does  it  jump  from  molecule  to  molecule,  or  does 
it  flow  in  the  interstices  ?  If  the  former,  pain  must  be  a 
solid;  if  the  latter,  it  must  be  a  fluid;  both  of  which 
hypotheses  are  manifestly  nonsense.  There  is  a  third  alter- 
native. It  may  be  a  movement  communicated  from  molecule 
to  molecule.  .  .  .  Consider  again.  Imagine  the  molecules 
of  the  nerve  swinging  in  space.  Now  imagine  a  wider  swing. 
Does  that  resemble  pain  ?  Turn  the  circle  into  a  spiral.  Is 
that  like  pain  ?  But  it  may  be  said,  Pain,  we  know,  is  not 
really  in  the  nerves,  it  is  in  the  brain.  Again  the  same 
problem  awaits  us.  The  brain  is  made  of  cells  and  fibres. 
Is  pain  in  the  cells  ?  Is  it  in  the  fibres  ?  In  either  case  we 
must  come  down  to  molecules  at  last,  and  again  the  pain 
eludes  our  search.  No  conceivable  form  of  matter  and  no- 
conceivable  movement  of  matter  bears  the  smallest  resem- 
blance to  pain,  or  can  by  any  human  imagination  be  assimi- 
lated to  pain.  We  are  driven  to  the  conclusion  that  pain 
and  matter  are  things  with  no  community  of  nature,  are 
facts  of  totally  different  orders,  and  cannot  be  reduced  to 
any  common  term.  Pain  is  neither  in  the  nerves,  nor  in  the 
brain,  nor  in  any  position  in  space.  It  is  in  the  mind." 
And  of  course  this  expression  '  in  the  mind  '  simply  means 
that  we  feel  it. 

Fallacies  of  False  Analogy  may  often  be  regarded  as  cases 
of  an  ill-conceived,   and    perhaps  of  a  confused,   universe 


210  THE   ILL-CONCEIVED   UNIVERSE. 

The  bare  facts  or  some  of  them  may  be  known  accurately 
enough,  but  the  relations  between  them — the  general  back- 
ground in  which  they  are  set — is  conceived  erroneously. 
"  Carlyle's  saying  that  a  ship  could  never  be  taken  round 
Cape  Horn  if  the  crew  were  consulted  every  time  the  captain 
proposed  to  alter  the  course,  if  taken  seriously  as  an  analog- 
ical argument  against  Representative  Government,  is  open 
to  the  objection  that  the  differences  between  a  ship  and  a 
State  are  too  great  for  any  argument  from  the  one  to  the 
other  to  be  of  value.  It  was  such  fallacious  analogies  as 
these  that  Heine  had  in  view  in  his  humorous  prayer, 
'  Heaven  defend  us  from  the  Evil  One  and  from  meta- 
phors '. "  * 

Often  as  we  turn  from  one  aspect  of  a  situation  to  another 
we  find  some  new  fact  which  is  not  consistent  with  some 
general  statement  that  we  made  about  the  first  aspect;  and 
this  may  lead  to  a  ''bull'.  'One  man  is  as  good  as 
another  ',  says  the  Irishman  when  he  resents  the  claim  of 
superiority  made  by  some  one  else;  but  as  he  thinks  of  his 
own  excellences  and  the  other's  shortcomings  he  adds,  '  and 
sometimes  a  long  sight  better '.  Sometimes  the  bull  is  due 
to  an  unfortunate  metaphor;  e.g. ,  '  Our  cup  of  sorrow  is 
overflowing,  and  is  not  yet  full '. 

Since  every  metaphor  rests  on  the  assumption,  though  even 
for  only  a  moment,  of  a  kind  of  universe,  every  case  of  mixed 
metaphors  is  a  case  of  confused  universes.  I  take  the  follow- 
ing from  Genung's  "  Rhetoric  "  :  "  The  very  recognition  of 
these  or  any  of  them  by  the  jurisprudence  of  a  nation  is  a 
mortal  wound  to  the  very  keystone  upon  which  the  whole  arch 
of  morality  reposes." — "  This  world  with  all  its  trials  is  the 
furnace  through  which  the  soul  must  pass  and  be  developed 
before  it  is  ripe  for  the  next  world." — "  I  write  to  you  in  a 
state  of  mind  that  I  really  ardly  know  what  I  am  about,  but 
I  cannot  indure  making  no  effort  to  clear  up  the  gaping  abiss 

*  Min to' s  "Logic",  p.  373. 


THE   NEGLECTED   ASPECT.  211 

which  the  events  of  the  past  fatal  afternoon  has  raised  between 
us." 

Another  kind  of  ill-conceived  universe  may  be  called  the 
Universe  with  a  Neglected  Aspect.  This  phrase  is  intended 
to  include  all  arguments  in  which  the  existence  or  influence 
of  some  essential  relation  or  object  in  the  uni-  Theneg- 
verse  involved  is  neglected.  In  calculating  the  lected aspect- 
time  it  will  take  a  feather  dropped  from  the  window  to 
reach  the  ground  we  have  a  right  to  neglect  the  attraction 
exerted  upon  the  feather  by  some  fixed  star,  for  though 
there  is  such  an  attraction  it  makes  no  appreciable  differ- 
ence in  the  result,  and  we  have  a  right  to  neglect  the  death 
of  some  Asiatic  despot,  for  it  makes  no  difference  at  all  in 
the  result — is  not  in  the  universe  under  consideration.  But 
we  have  no  right  to  neglect  the  resistance  of  the  air,  or  the 
influence  of  the  wind  with  all  its  gusts  and  eddies;  for  they 
make  every  possible  difference  in  the  result.  Similarly  we 
have  no  right  to  conclude  that  free  trade  is  necessarily  the 
best  policy  for  some  particular  state,  merely  because  it  is 
always  or  usually  the  policy  most  favorable  for  the  accumu- 
lation of  wealth,  unless  we  have  first  made  sure  that  there 
is  no  question  of  education,  or  public  morals,  or  military 
necessity,  or  international  politics,  which  demands  some 
other  policy. 

Every  roseate  picture  of  the  happiness  to  be  attained  when 
the  competition  of  commercial  rivals  has  ceased,  and  the 
State  controls  all  industry  and  gives  every  one  his  due,  is 
painted  in  happy  forgetfulness  of  the  natural  discontent, 
selfishness,  laziness,  or  ambition  which  would  prompt  most 
of  the  people  in  such  a  community  to  shirk  their  appointed 
tasks,  to  use  personal  influence  in  order  to  get  some  special 
privilege,  or  to  gain  control  of  the  machinery  of  government 
for  the  particular  benefit  of  themselves  and  their  friends, — 
forces  in  human  nature  which  would  replace  commercial 
competition  with  political  jobbery. 

Under   the    head    of    Composition,    What  el  y   gives    several 


212  THE   ILL-CONCEIVED   UNIVERSE. 

examples  of  what  I  should  rather  call  a  neglected  relation  of 
articulation : 

"  There  is  no  fallacy  more  common  or  more  likely  to 
deceive  than  the  one  before  us:  the  form  in  which  it  is  most 
usually  employed  is  to  establish  some  truth,  separately, 
concerning  each  single  member  of  a  certain  class,  and  then 
to  infer  the  same  of  the  whole  collectively;  thus  some  infidels 
have  labored  to  prove  concerning  some  one  of  our  Lord's 
miracles,  that  it  might  have  been  the  result  of  the  accidental 
conjuncture  of  natural  circumstances;  next  they  endeavor 
to  prove  the  same  concerning  another,  and  so  on ;  and 
thence  infer  that  all  of  them  might  have  been  so.  They 
might  argue  in  like  manner,  that  because  it  is  not  very  im- 
probable that  one  may  throw  sixes  in  any  one  out  of  a 
hundred  throws,  therefore  it  is  no  more  improbable  that  one 
may  throw  sixes  a  hundred  times  running." 

This  is,  as  we  have  said,  a  case  of  neglected  articulation. 
The  miracles  in  question  all  took  place  within  a  certain  short 
period  and  were  all  connected  with  a  single  personality. 
The  general  fact  that  one  supposed  miracle  is  shown  to  be 
the  result  of  accident  would  be  a  reason  for,  and  not  against, 
the  belief  that  a  great  many  others  could  be  explained  in  the 
same  way;  but  if  these  others  are  accidents  and  not  really 
miracles  we  should  expect  to  find  them  scattered,  not 
grouped  and  articulated  as  they  are  in  the  case  in  question. 
So  with  the  throws  of  sixes.  It  is  not  the  occurrence  of  a 
hundred  of  them  that  is  remarkable,  but  of  a  hundred  in 
succession  with  the  same  dice  and  in  the  hands  of  the  same 
player.* 

*  This  argument  of  Whately's  is  perfectly  valid  as  a  reply  to  those 
who  try  to  explain  the  miracles  in  question  by  a  series  of  physical  acci- 
dents. But  if  it  be  taken  as  an  independent  proof  of  their  miraculous 
nature  it  might  be  itself  regarded  as  an  example  of  the  Neglected  Aspect; 
for  it  fails  to  consider  the  mental  influences  which  tend  to  produce  this 
very  grouping.  It  is  easier  to  hypnotize  one  person  if  others  have  been 
hypnotized  in  his  presence,  and  for  much  the  same  reason  the  'cures' 
•wrought  by  our  modern  faith  doctors  generally  come  in  groups. 


THE   NEGLECTED   ASPECT.  213 

Often  the  neglected  relation  is  one  that  is  necessarily  and 
obviously  involved  in  some  general  scheme  that  is  contem- 
plated, and  the  neglect  to  consider  it  must  be  charged,  not 
to  ignorance,  but  to  sheer  haste  and  carelessness.  "  From 
the  circumstance  that  some  men  of  humble  station,  who 
have  been  well  educated,  are  apt  to  think  themselves  above 
low  drudgery,  it  is  argued  that  universal  education  of  the 
lower  orders  would  beget  general  idleness;  this  argument 
rests,  of  course,  on  the  assumption  of  parallelism  in  the  two 
cases,  viz.,  the  past  and  the  future;  whereas  there  is  a  cir- 
cumstance that  is  absolutely  essential,  in  which  they  differ; 
for  when  education  is  universal 'it  must  cease  to  be  a  distinc- 
tion; which  is  probably  the  very  circumstance  that  renders 
men  too  proud  for  their  work. "  * 

This  blunder  is  like  that  of  the  people  who  clamor  for 
some  change  in  the  tariff  or  in  the  currency  that  will  give 
everybody  '  more  money  ',  forgetting  that  if  dollars  were  as 
common  as  pebbles  they  would  be  worth  no  more  than 
pebbles,  and  all  that  one  could  carry  would  hardly  buy  a 
dinner;  or  like  that  committed  by  the  member  of  a  crowded 
audience  who  asked  that  everybody  present  might  be  allowed 
to  stand  on  the  back  of  his  seat  and  thus  get  an  unobstructed 
view  of  the  performance. 

The  blunder  of  a  Neglected  Aspect  is  involved  in  every 
philosophical  theory  which  resolves  all  reality  into  mere 
phenomena,  forgetting  that  there  can  be  no  phenomenon  or 
appearance  without  something  to  appear  and  some  one  to 
whom  it  appears.  It  is  involved  in  the  old  myth  of  Atlas 
supporting  the  world:  for  any  object  that  requires  to  be 
supported  does  so  because  it  is  heavy,  i.e.,  because  it  is 
attracted  by  every  other  object  and  therefore  tends  to  move 
towards  the  common  centre  of  gravity.  But  as  there  is 
nothing  outside  of  the  world  (or  at  least  outside  of  the  uni- 
verse) towards  which  it  is  attracted,  the  universe  as  a  whole 

*  Whately,  op.  cit. 


214  THE   ILL-CONCEIVED    UNIVERSE. 

does  not  tend  to  fall,  or  in  other  words,  it  has  no  weight  at 
all.  Another  such  absurdity  is  involved  in  the  question 
'  Where  is  the  universe  ?  '  To  tell  the  position  of  any  par- 
ticular object  is  to  tell  how  it  lies  with  reference  to  some 
other  object  or  objects;  but  the  universe  contains  all  objects 
— it  would  not  be  the  universe  if  it  did  not — and  therefore 
there  is  nothing  lying  outside  of  it  by  which  it  can  be 
located  :  it  has  no  place.  What  has  been  said  about  the  place 
of  the  world  is  applicable,  mutatis  mutandis,  to  questions 
about  its  cause  and  the  time  at  which  it  came  into  existence. 
A  similar  criticism  can  be  applied  to  the  question  '  Is  life 
•worth  living  ?  '  To  ask  what  a  thing  is  worth  is  to  ask  what 
people  are  willing  to  take  in  exchange  for  it — what  other 
object  they  believe  will  give  them  as  much  satisfaction.  But 
all  exchange,  all  weighing  of  alternatives,  all  satisfaction  and 
dissatisfaction  presuppose  a  life  in  which  they  take  place, 
and  to  ask  what  this  life  itself  is  worth  is  as  absurd  as  to  try 
to  weigh  your  balances  in  their  own  pan. 

In  all  such  cases  the  universe  as  a  whole — the  total  system 
of  related  objects — is  spoken  of  as  though  it  could  possess 
relations  which  exist  only  between  various  members  within 
it. 

Dilemmas  of  the  epigrammatic  sort  are  almost  always  based 
upon  a  view  of  only  half  the  universe,  and  for  this  reason 
"  can  often  be  retorted  by  producing  as  cogent  a  dilemma  to 
the  contrary  effect.  Thus  an  Athenian  mother,  according 
to  Aristotle,  addressed  her  son  in  the  following  words:  '  Do 
not  enter  into  public  business;  for  if  you  say  what  is  just, 
men  will  hate  you;  and  if  you  say  what  is  unjust,  the  gods 
will  hate  you  '.  To  which  Aristotle  suggests  the  following 
retort:  '  I  ought  to  enter  into  public  affairs;  for  if  I  say  what 
is  just,  the  gods  will  love  me;  and  if  I  say  what  is  unjust, 
men  will  love  me. '  '  (Jevons.)  Again,  Kpictetus  says  that 
if  honors  which  we  do  not  possess  are  good,  we  should  rejoice 
that  another  has  them;  if  bad,  that  we  have  them  not.  But 
a  pessimist  might  reply  that  if  they  are  good,  we  should  grieve 


THE   NEGLECTED   MEMBER.  215 

that  we  have  them  not;  if  bad,  that  another  has  them. 
What  Epictetus  says,  therefore,  amounts  merely  to  this:  that 
we  should  look  on  the  bright  side  of  things  and  deliberately 
ignore  the  other  side.  This  certainly  is  a  healthy  practical 
attitude,  but  when  one  begins  to  theorize  he  must  see  both 
sides. 

Often,  as  Lotze  points  out,*  an  aspect  of  a  situation, 
though  mentioned,  can  be  crowded  out  of  view  by  the  mere 
order  of  a  sentence.  To  say  '  I  am  a  great  deal  better  off 
than  he  is  '  is  more  cheerful  than  to  say  '  He  is  worse  off 
than  I  am  ';  but  the  facts  of  the  case  are  the  same.  This  is 
so  also  with  the  saying  '  There  is  a  silver  lining  to  every 
cloud  '  and  its  converse,  '  There  is  a  cloud  to  many  a  silver 
lining  '.  ;'  Think  of  public  teachers  who  say  that  the  farmer 
is  ruined  by  the  cost  of  transportation,  when  they  mean  that 
he  cannot  make  any  profits  because  his  farm  is  too  far  from 
the  market. "  f 

When  the  whole  background  is  not  misconceived  or  dis- 
torted or  a  part   of  it  overlooked,  we  may  still   err  by  over- 
looking some  member  of  the  universe,  coordinate 
with   those    under    discussion,    whose    influence    neglected 
(or  at  least  whose  presence)  ought  to  have  been 
taken  into  account.      If  A,  B,  C,  and  D  are  fixed  points  on 
a  given  plane,  I  may  be  able  to  determine  the  relations  of  any 
one  of  them  to  any  other  without  any  reference  to  the  rest ;  but 
if  they  are  planets,  each  attracting  every  other,  I   cannot  do 
this.     If  any  member  of  the  system  is  ignored,  any  prediction 
I  may  make  with  reference  to  the  others  is  bound   to  turn 
out  more  or  less  erroneous.     It  is  here  that  we  find  the  fallacy 

*  '•  It  may  be  said  that  evil  appears  only  in  particulars,  and  that  when 
we  take  a  comprehensive  view  of  the  great  whole  it  disappears;  but  of 
what  use  is  a  consolation  the  power  of  which  depends  upon  the  arrange- 
ment of  clauses  in  a  sentence  ?  For  what  becomes  of  our  consolation  if 
we  convert  the  sentence  which  contains  it  thus — The  world  is  indeed 
harmonious  as  a  whole,  but  if  we  look  nearer  it  is  full  of  misery  ?  "  Mi- 
crocosmus,  Bk.  IX,  Ch.  V  (Scribners). 

•j-  Sunnier,  op.  cit.,  p.  46. 


216  THE   ILL-CONCEIVED   UNIVERSE. 

of  the  old  argument  in  favor  of  a  protective  tariff,  '  Gold  and 
silver  are  wealth;  a  protective  tariff,  'by  shutting  out  imports 
while  not  interfering  with  exports,  increases  the  gold  and 
silver  in  a  country;  it  therefore  increases  the  country's 
wealth.'  Assuming  the  truth  of  the  premises,  the  conclusion 
does  not  follow,  because  while  gold  and  silver  are  wealth 
they  are  not  the  only  forms  of  wealth,  and  the  imported  gold 
and  silver  must  be  paid  for  by  some  other  kind  of  wealth 
exported.  The  fallacy  lies  in  forgetting  this  exported 
wealth — in  looking  at  only  a  part  of  the  universe  or  system 
in  question. 

So,  many  an  unfortunate  maintains  that  he  '  has  a  right  to 
a  living  ',  or  to  certain  comforts;  forgetting  that  such  a  right 
on  his  part  implies  a  duty  to  provide  him  with  these  things 
on  the  part  of  somebody  else. 

The  best  account  that  I  know  of  this  fallacy  of  the  for- 
gotten member  of  the  universe  is  to  be  found  in  the  little 
book  by  Professor  Sumner  already  quoted. 

"  THE    FORGOTTEN    MAX." 

"  In  all  jobbery  the  case  is  the  same.  There  is  a  victim 
somewhere  who  is  paying  for  it  all.  The  doors  of  waste  and 
extravagance  stand  open,  and  there  seems  to  be  a  general 
agreement  to  squander  and  spend.  It  all  belongs  to  some- 
body. There  is  somebody  who  had  to  contribute  it,  and 
who  will  have  to  find  more.  Nothing  is  ever  said  about 
him.  Attention  is  all  absorbed  by  the  clamorous  interests, 
the  importunate  petitioners,  the  plausible  schemers,  the 
pitiless  bores.  Now,  who  is  the  victim  ?  He  is  the  For- 
gotten Man.  If  we  go  to  find  him,  we  shall  find  him  hard 
at  work  tilling  the  soil  to  get  out  of  it  the  fund  for  all  the 
jobbery,  the  object  of  all  the  plunder,  the  cost  of  all  the 
economic  quackery,  and  the  pay  of  all  the  politicians  and 
statesmen  who  have  sacrificed  his  interests  to  his  enemies. 
We  shall  find  him  an  honest,  sober,  industrious  citizen, 
unknown  outside  his  little  circle,  paying  his  debts  and  his 


THE   NEGLECTED   MEMBER.  217 

taxes,    supporting  the  church  and  the  school,    reading  his 
party  newspaper,  and  cheering  for  his  pet  politician. 

"  We  must  not  overlook  the  fact  that  the  Forgotten  Man 
is  not  infrequently  a  woman.  I  have  before  me  a  newspaper 
which  contains  five  letters  from  corset-stitchers  who  complain 
that  they  cannot  earn  more  than  seventy-five  cents  a  day 
with  a  machine,  and  that  they  have  to  provide  the  thread. 
The  tax  on  the  grade  of  thread  used  by  them  is  prohibitory 
as  to  all  importation,  and  it  is  the  corset-stitchers  who  have 
to  pay  day  by  day  out  of  their  time  and  labor  the  total 
enhancement  of  price  due  to  the  tax.  Women  who  earn 
their  own  living  probably  earn  on  an  average  seventy- five 
cents  per  day  of  ten  hours.  Twenty-four  minutes'  work 
ought  to  buy  a  spool  of  thread  at  the  retail  price,  if  the 
American  workwoman  were  allowed  to  exchange  her  labor 
for  thread  on  the  best  terms  that  the  art  and  commerce  of 
to-day  would  allow;  but  after  she  has  done  twenty-four 
minutes'  work  for  the  thread  she  is  forced  by  the  laws  of  her 
country  to  go  back  and  work  sixteen  minutes  longer  to  pay 
the  tax — that  is  to  support  the  thread-mill.  The  thread- 
mill,  therefore,  is  not  an  institution  for  getting  thread  for  the 
American  people,  but  for  making  thread  harder  to  get  than 
it  would  be  if  there  were  no  such  institution.  ...  It  makes 
a  great  impression  on  the  imagination,  however,  to  go  to  a 
manufacturing  town  and  see  great  mills  and  a  crowd  of 
operatives;  and  such  a  sight  is  put  forward,  under  the  special 
allegation  that  it  would  not  exist  but  for  the  protective  tax,  as  a 
proof  that  protective  taxes  are  wise.  But  if  it  be  true  that 
the  thread-mill  would  not  exist  but  for  the  tax,  then  how 
can  we  form  a  judgment  as  to  whether  the  protective 
system  is  wise  or  not  unless  we  call  to  mind  all  the  seam- 
stresses, washerwomen,  servants,  factory-hands,  saleswomen, 
teachers,  and  laborers'  wives  and  daughters,  scattered  in  the 
garrets  and  tenements  of  great  cities  and  in  cottages  ail  over 
the  country,  who  are  paying  the  tax  which  keeps  the  mill 
going  and  pays  the  extra  wages  ?  If  the  sewingwomen. 


2i8  THE   ILL-CONCEIVED   UNIVERSE. 

teachers,  and  washerwomen  could  once  be  collected  over 
against  the  thread-mill,  then  some  inferences  could  be  drawn 
which  would  be  worth  something.  Then  some  light  might 
be  thrown  upon  the  obstinate  fallacy  of  '  creating  an  indus- 
try ',  and  we  might  begin  to  understand  the  difference 
between  wanting  thread  and  wanting  a  thread-mill.  Some 

O  O 

nations  spend  capital  on  great  palaces,  others  on  standing 
armies,  others  on  iron-clad  ships  of  war.  Those  things  are 
all  glorious,  and  strike  the  imagination  with  great  force  when 
they  are  seen;  but  no  one  doubts  that  they  make  life  harder 
for  the  scattered  insignificant  peasants  and  laborers  who  have 
to  pay  for  them  all.  They  '  support  a  great  many  people  ', 
they  '  make  work  ',  they  '  give  employment  to  other  indus- 
tries '.  We  Americans  have  no  palaces,  armies,  or  iron-clads, 
but  we  spend  our  earnings  on  protected  industries.  A  big 
protected  factory,  if  it  really  needs  the  protection  for  its 
support,  is  a  heavier  load  for  the  Forgotten  Men  and  Women 
than  an  iron-clad  ship  of  war  in  time  of  peace. 

"It  is  plain  that  the  Forgotten  Man  and  the  Forgotten 
Woman  are  the  real  productive  strength  of  the  country. 
The  Forgotten  Man  works  and  votes — generally  he  prays — 
but  his  chief  business  in  life  is  to  pay.  His  name  never  gets 
into  the  newspapers  except  when  he  marries  or  dies.  He  is 
an  obscure  man.  He  may  grumble  sometimes  to  his  wife, 
but  he  does  not  frequent  the  grocery,  and  he  does  not  talk 
politics  at  the  tavern.  So  he  is  forgotten.  Yet  who  is  there 
whom  the  statesman,  economist,  and  social  philosopher 
ought  to  think  of  before  this  man  ?  If  any  student  of  social 
science  comes  to  appreciate  the  case  of  the  Forgotten  Man, 
he  will  become  an  unflinching  advocate  of  strict  scientific 
thinking  in  sociology,  and  a  hard-hearted  sceptic  as  regards 
any  scheme  of  social  amelioration.  He  will  always  want  to 
know,  Who  and  where  is  the  P'orgotten  Man  in  this  case, 
and  who  will  have  to  pay  for  it  all  ?  "  * 

*  Sumner.  op.  cit.,  pp.   145-149. 

Since  the  forgotten  member  is  always  a  member  related    to  the  rest  of 


THE   NEGLECTED   WHOLE.  219 

The  examples  so  far  given  have  all  shown  a  universe 
unduly  curtailed  or  simplified  through  the  neglect  to  con- 
sider some  one  or  more  of  its  essential  relations 

The 
or  members.      But  there  are  cases  in  which  the   neglected 

whole. 

very  existence  of  a  universe  of  interrelated  mem- 
bers seems   to  be  ignored.     To  quote  Whately  once  more 
(though    here    again    he  gave  the  example  under   another 
head) : 

"When  a  multitude  of  particulars  are  presented  to  the 
mind,  many  are  too  weak  or  too  indolent  to  take  a  compre- 
hensive view  of  them;  but  confine  their  attention  to  each 
single  point,  by  turns:  and  thus  decide,  infer,  and  act 
accordingly:  e.g.,  the  imprudent  spendthrift,  finding  that 
he  is  able  to  afford  this,  or  that,  or  the  other  expense,  forgets 
that  all  of  them  together  will  ruin  him. 

'  To  the  same  head  may  be  reduced  that  fallacious 
reasoning  by  which  men  vindicate  themselves  to  their  own 
conscience  and  to  others,  for  the  neglect  of  those  undefined 
duties,  which  though  indispensable,  and  therefore  not  left  to 
our  choice  whether  we  will  practise  them  or  not,  are  left  to 
our  discretion  as  to  the  mode,  and  the  particular  occasions, 
of  practising  them;  e.g.,  '  I  am  not  bound  to  contribute  to 
this  charity  in  particular;  nor  to  that;  nor  to  the  other': 
the  practical  conclusion  which  they  draw  is,  that  all  charity 
may  be  dispensed  with." 

In  each  of  these  cases  the  trouble  lies,  as  Whately  so 
clearly  says,  in  the  failure  to  "  take  a  comprehensive  view  " 
of  the  universe  as  a  whole.  In  the  former  case  we  forget 
that  when  a  given  variable  (namely,  the  money  at  one's 
disposal)  is  placed  there  it  cannot  also  be  placed  here;  in 
the  latter  we  forget  that  if  the  variable  (namely,  charity)  is 
not  placed  there,  it  ought  to  be  placed  here,  since  it  ought 
to  have  a  place  somewhere  or  other  in  the  universe. 

The  same  failure  to  keep  the  whole  universe  and  its  rela- 

the  system,  no  hard  and  fast  line  can  be  drawn  between  a  case  of  the 
forgotten  member  and  a  case  of  the  forgotten  relation. 


220  THE   ILL-CONCEIVED   UNIVERSE. 

tions  in  view  accounts  for  what  Whately  calls  the  Fallacy  of 
Objections,  i.e.,  "  showing  that  there  are  objections  against 
some  plan,  theory,  or  system,  and  thence  inferring  that  it 
should  be  rejected;  when  that  which  ought  to  have  been 
proved  is,  that  there  are  more,  or  stronger,  objections  against 
the  receiving  than  the  rejecting  of  it.  ...  For  there  never 
was,  nor  will  be,  any  plan  executed  or  proposed,  against 
which  strong  and  even  unanswerable  objections  may  not  be 
urged;  so  that  unless  the  opposite  objections  be  set  in  the 
balance  on  the  other  side,  we  can  never  advance  a  step." 

This  Fallacy  of  Objections  is  peculiarly  characteristic  of 
people  whose  energy  is  small  but  whose  moral  or  aesthetic 
sensibilities  are  morbidly  developed.  They  should  help  to 
pay  a  detective  to  catch  a  thief,  and  refuse  because  a  detec- 
tive's work  is  not  straightforward  and  frank;  they  should 
help  to  hang  a  murderer,  or  should  shoot  a  murdering 
burglar  to  secure  the  safety  of  honest  people,  and  hold  back 
because  it  is  cruel ;  they  want  the  liquor  traffic  cut  down 
and  they  are  convinced  that  a  license  system  is  the  only  thing 
that  will  do  it,  but  they  object  to  this  because  it  makes  the 
government  'a  partner  in  sin';  they  should  wash  their 
clothes,  but  they  are  afraid  of  soiling  their  lingers.  Perhaps 
there  is  some  relation  in  life  in  which  each  of  us  strains  for 
ever  at  gnats  and  swallows  camels.  We  see  the  gap  in  the 
universe,  but  there  is  no  ideal  material  at  hand,  so  we  let  it 
go  unfilled : 

"  Our  common  problem,  yours,  mine,  every  one's, 
Is.  not  to  fancy  what  were  fair  in  life 
Provided  it  could  be,  but  finding  first 
What  can  be,  then  find  how  to  make  it  fair 
Up  to  our  means  ;  a  very  different  thing." 


CHAPTER  XXL 

THE  DIFFERENCE  BETWEEN  INDUCTION  AND  DEDUCTION. 

THE  student  who  has  followed  the  preceding  chapters  at 
all  thoughtfully  has  doubtless  been  impressed  by  a  keen  and 
disappointing  sense  of  limitation  :  there  are  so  many  things 

that  we  must  not  do.  and  so  few  that  we  may.  so 

.     .  ,        ,       ,  ,          -  .      Difference 

many  cautions  to  hold  us  back,  and  so  few  posi-   in 

.    .  ,     ,  r^,.     .  .         limitations, 

tive  principles  to  help  us  on.      Ihis  impression 

is  well  founded.  The  principles  of  deductive  logic  are  im- 
portant indeed  and  should  never  be  forgotten  :  and  yet  if  any 
one  dwells  on  them  exclusively,  and  forgets  that  cautions 
would  be  worthless  in  the  absence  of  some  positive  forward 
impulse,  he  is  likely  to  become  a  mere  carping  critic  ;  a  fault- 
finder, who  is  forever  detecting  flaws  in  the  reasoning  of 
others,  but  utterly  incapable  of  doing  any  constructive  work 
of  his  own. 

Induction  is  that  part  of  logic  which  is  concerned  with  the 
onward  movement  that  deduction  cannot  undertake.  Its 
essential  task  can  be  best  understood  by  looking  once  more 
at  the  limitations  of  the  syllogism  and  then  seeing  how  it 
tries  to  supplement  them.  The  first  figure  teaches  that  if 
every  A  is  a  B  and  every  B  is  a  C,  it  is  safe  to  conclude  that 
every  A  is  a  C.  But  it  does  not  tell  how  to  find  out  in  the 
first  place  that  every  A  is  a  B  or  that  every  B  is  a  C.  It 
proceeds  in  this  case,  as  they  say,  from  generals  to  particu- 
lars, but  not  from  particulars  to  generals.  Induction  tells  us 
how  to  prove  in  the  first  place  that  every  A  is  a  B  or  that 

221 


222  INDUCTION   AND   DEDUCTION. 

every  B  is  a  C  ;  how  to  get  from  particulars  to  generals. 
The  second  figure  teaches  that  dissimilarity  proves  objects 
not  to  be  identical ;  but  it  does  not  help  us  to  prove  that  ob- 
jects are  identical.  Induction  does.  The  third  figure  teaches 
that  the  coexistence  of  relations  proves  that  they  are  com- 
patible, that  they  may  come  together  ;  but  it  does  not  try 
to  prove  that  they  are  necessarily  connected,  so  that  they  must 
come  together.  Induction  does.  Thus  in  the  case  of  each 
figure  induction  attempts  a  task  in  the  presence  of  which  de- 
duction is  helpless.  This  work  of  getting  more  general  or 
more  positive  or  more  emphatic  results  than  those  reached  by 
the  syllogism  is  not  the  whole  of  inductive  logic  any  more 
than  the  syllogism  itself  is  the  whole  of  deductive  ;  but,  like 
the  syllogism  in  deduction,  it  is  the  heart  of  the  subject.* 

Why  Induction  is  able  to  go  ahead  and  do  more  than  De- 
duction we  shall  understand  better  when  we  have  reached  the 
close  of  the  next  chapter,  and  better  still  when  we  have  gone 
farther.  But  there  are  four  things  about  Induction  by  which 
we  can  explain  at  least  a  part  of  the  difference  now. 

In  the  first  place,  every  system  of  Induction  rests  on  the 
assumption  that  facts  of  true  logical  significance  can  be  attained 
by  direct  observation.  If  a  person  whose  mental  life  was 
limited  to  deductive  reasoning  were  asked  whether  the  man 
in  front  of  him  had  light  hair  or  dark,  he  might  be  in  posses- 
sion of  some  premises  that  would  enable  him  to  answer  the 
question  or  he  might  not ;  and  if  he  had  no  such  premises,  he 

*  It  is  -often  said  that  the  difference  between  Deduction  and  Induction 
is  that  the  one  proceeds  from  generals  to  particulars,  while  the  other  pro- 
ceeds from  particulars  to  generals;  that  is  to  say,  that  deduction  pro- 
ceeds from  statements  about  classes  of  things  to  statements  about  smaller 
classes  or  about  individuals,  while  induction  proceeds  from  statements 
about  individuals  to  statements  about  classes.  Hut  in  deduction  it  is  only 
the  first  figure  of  the  syllogism  that  goes  from  statements  about  classes  to 
statements  about  the  individuals  in  them;  and  in  induction  it  is  only  the 
process  corresponding  to  the  first  figure  that  is  concerned  with  mere 
generalization.  This  statement,  therefore,  is  based  upon  too  narrow  a 
view  of  the  scope  of  both  branches  of  Logic. 


DIFFERENCE   IN   LIMITATIONS.  223 

could  not  answer  it.  But  the  one  thing  which  he  could  not 
do  would  be  to  look  at  the  man  and  see.  Reasoning  abso- 
lutely limited  to  deduction  is  eminently  suited  to  people  like 
the  monastic  scholars  of  the  middle  ages  who  did  not  profess 
to  possess  any  other  source  of  true  knowledge  than  the  writ- 
ten word  of  the  Church  as  found  in  some  recognized  author- 
ity, such  as  the  Bible  or  the  works  of  Aristotle  or  St.  Thomas. 
To  the  orthodox  Scholastic  every  opinion  at  variance  with 
such  authorities  was  not  only  false  but  wicked.  "  There  is  a 
characteristic  anecdote  of  Scheiner,  who  contests  with  Galileo 
the  honor  of  being  the  first  to  observe  the  spots  in  the  sun. 
Scheiner  was  a  monk;  and,  on  communicating  to  the  superior 
of  his  order  the  account  of  the  spots,  he  received  in  reply 
from  that  learned  father  a  solemn  admonition  against  such 
heretical  notions:  'I  have  searched  through  Aristotle,'  he 
said,  '  and  can  find  nothing  of  the  kind  mentioned  ;  be 
assured,  therefore,  that  it  is  a  deception  of  your  senses  or  of 
your  glasses.'  "  *  Thus,  to  the  Scholastic,  the  data  for  reason- 
ing were  all  given  by  some  authority,  and  usually  in  the  form 
of  general  propositions.  In  contrast  with  this,  Induction 
supposes  us  to  be  set  loose  in  the  world  with  all  our  senses 
about  us  to  collect  our  own  data;  to  find  the  straw  as  well 
as  to  make  the  bricks. 

Now  all  observation  is  of  individual  facts.  General  truths 
may  be  inferred  ;  but  the  facts  on  which  they  are  (or  should 
be)  based  must  be  observed  one  at  a  time.  Consequently, 
•while  the  Deductive  reasoner  is  accustomed  to  appeal  for  the 
most  part  to  general  principles  of  some  sort  by  way  of  prem- 
ises, and  thus  learns  to  regard  such  principles  with  a  cer- 
tain veneration,  the  Inductive  reasoner  is  appealing  all  the 
time  to  individual  facts  as  revealed  by  the  senses,  and  he 
gives  a  large  share  of  his  veneration  to  them.  Hence  the 
saying  that  in  science  a  single  fact  is  worth  a  bushel  of  theorv. 

In  the  second  place,  Induction  distinctly  recognizes  the 

*  Baden  Powell's  "  History  of  Natural  Philosophy",  p.  171.  Quoted 
in  Fowler's  "Inductive  Logic",  p.  293. 


224  INDUCTION   AND   DEDUCTION. 

presence  of  change  in  the  world.  It  may  be  remembered  that 
the  relations  of  things  (as  distinguished  from  the  laws  01 
thought  pure  and  simple)  upon  which  deductive  reasoning 
turns  are  individual  identity,  similarity,  and  the  coexistence 
of  qualities  or  other  attributes.  .  Now  all  three  of  these  rela- 
tions could  exist — identity  after  a  fashion  and  the  other  two 
very  well — in  a  world  in  which  there  was  no  change,  in  which 
nothing  ever  happened  or  came  to  pass  ;  and  it  may  be  re- 
membered that  this  notion  of  change  was  so  remote  from  the 
conception  of  the  universe  involved  in  deduction  that  the 
rules  of  the  syllogism  have  been  declaring  for  centuries  that 
contrary  relations  prove  objects  to  be  non-identical,  without 
ever  stopping  to  say  that  this  rule  only  holds  when  the  objects 
in  question  are  observed  at  the  same  time,  or  at  least  nearly 
enough  at  the  same  time  to  make  it  certain  that  those  par- 
ticular relations  could  not  have  changed.  Induction  on 
the  other  hand  has  to  do  almost  altogether  with  a  world  of 
change;  and  for  it  the  most  important  relation  of  all  is  the 
relation  of  one  change  or  event  to  another. 

A  third  characteristic  of  induction  is  that  it  rests  at  bottom 
upon  a  tendency,  unconscious  or  conscious,  vague  or  definite, 
to  act  as  though  we  took  for  granted  that  in  the  changes 
and  other  relations  of  things  we  might  expect  a  certain  uni- 
formity. This  tendency  is  so  important  that  we  must  pre- 
sently give  a  longer  account  of  it. 

The  fourth  characteristic  of  Induction  is  that  when  it  reaches 
the  critical  stage  it  attempts  more  or  less  seriously  to  find  out 
and  examine  every  case  of  a  given  sort  in  the  world  or  the 
part  of  the  world  under  consideration.  Let  us  explain  this 
with  reference  to  each  of  the  figures  separately. 

If  we  wish  to  find  out  whether  it  is  true  that  every  mem- 
ber of  a  certain  family  has  light  hair,  the  simplest  inductive 
method  is  to  look  at  each  one  of  them,  and  if  we  find  none 
that  have  not  and  if  we  are  sure  that  we  have  examined  them 
all,  we  can  be  sure  that  the  statement  is  true.  In  this  way 
we  are  able  to  gain  the  singular  or  the  universal  proposition 


DIFFERENCE   IN   LIMITATIONS.  225 

which  is  required  as  one  of  the  premises  of  a  deductive  argu- 
ment in  the  first  figure. 

According  to  the  second  figure  dissimilarity  proves  that 
objects  are  not  identical,  but  similarity  does  not  prove  that 
they  are.  What  then  will  prove  it?  If  I  leave  a  book  of 
mine  in  a  library  and  the  next  day  find  one  there  which 
looks  precisely  like  it,  how  can  I  make  sure  that  it  is  mine, 
and  not  some  other  copy  of  the  same  work?  I  can  make 
sure  of  it  if  I  make  sure  that  no  book  has  gone  out  of  the 
library  since  mine  was  left  there,  and  then  examine  every 
book  in  it,  but  find  no  other  that  looks  precisely  like  the  one 
that  I  left.  Similarity  will  not  ordinarily  prove  identity,  for 
there  is  no  limit  to  the  number  of  things  that  may  resemble 
each  other  ;  but  if  we  are  certain  that  some  former  object 
still  exists  in  a  certain  part  of  the  world  and  still  retains  its 
former  appearance,  and  if  we  are  equally  certain  that  in  that 
part  of  the  world  there  is  now  only  one  object  with  that  ap- 
pearance, we  may  be  certain  that  the  two  are  identical.  Thus 
by  a  sufficiently  exhaustive  examination  of  other  things  we 
can  prove  the  identity  of  those  in  question,  where  the  second 
figure  of  the  syllogism  which  does  not  look  beyond  the  objects 
given  can  prove  only  non-identity. 

The  third  figure  proves  from  the  coincidence  of  two  given 
relations  that  they  are  compatible;  but  it  can  never  go  further 
and  prove  that  they  are  necessarily  connected.  Induction 
can  ;  and  again  it  proceeds  by  going  beyond  the  two  given 
relations  and  attempting  to  consider  a  worldful.  Suppose 
for  example  that  an  event  A  is  immediately  followed  by  the 
event  K.  For  deduction  this  proves  that  the  succession  of 
these  two  events,  A  and  K,  is  not  impossible  ;  and  for  induc- 
tion this  one  case  taken  by  itself  proves  nothing  more.  But 
if  we  assume,  as  induction  does,  that  every  event  has  a 
cause  with  which  it  is  necessarily  connected,  and  if  there  is 
anyway — whether  direct  or  indirect — of  going  overall  the 
events  which  preceded  K  and  of  showing  that  there  was  no 
event  but  A  which  could  have  caused  it,  then  we  can  be 


225  INDUCTION   AND   DEDUCTION. 

quite  sure  that  A  did  cause  it.  And  something  of  this  sort  is 
what  induction  attempts. 

Thus  there  is  an  inductive  process  corresponding  to  each 
figure  of  the  syllogism,  and  in  each  case  the  inductive  process 
attempts  to  reach  conclusions  which  the  deductive  does  not, 
by  looking  beyond  a  mere  pair  of  given  relations  and  at- 
tempting to  exhaust  the  universe. 

One  of  the  most  obvious  differences  between  deduction 
and  induction  is  that  in  deduction  any  conclusion  that  fol- 
lows from  the  given   premises  at  all  seems  to  fol- 
JMfference 

in  low  with  absolute  certainty,   while  in   inductive 

certainty.  .......  . 

reasoning   it  only  follows  with  a  greater  or  less 

degree  of  probability.  This  difference  is  striking  and  im- 
portant, and  it  is  sometimes  thought  to  depend  upon  some 
absolutely  fundamental  difference  between  the  two  methods. 
But  it  does  not.  So  far  as  the  strictly  demonstrative  side  of 
the  two  is  concerned  their  problems  are  precisely  the  same, 
namely  :  to  find  whether  the  conditions  named  in  the  pre- 
mises could  exist  in  the  assumed  universe  in  the  absence  of 
the  conditions  named  in  the  conclusion.  The  difference  in 
certainty  is  due  merely  to  the  greater  complexity  of  the  ma- 
terial which  induction  attempts  to  handle.  In  the  first  place, 
the  relations  of  things — the  laws  of  the  universe — which  in- 
duction has  to  assume  are  more  complex  ;  in  induction  we 
must  reckon  with  the  uniformity  of  nature  and  all  that  that 
implies  as  well  as  with  the  simpler  relations  of  things  assumed 
in  deduction.  Then,  in  the  second  place,  the  particular 
facts  that  have  to  be  built  together  according  to  the  general 
relations  of  our  universe  are — as  we  have  seen — ever  so  much 
more  numerous  in  induction — often  indeed  innumerable,  and 
even  when  we  know  that  all  the  facts  are  in  our  possession 
it  is  a  much  more  difficult  and  uncertain  thing  to  realize  how 
they  must  all  fit  together  when  there  are  a  great  number  of 
them  than  when  there  are  only  two.  Moreover,  in  induc- 
tion, where  the  ideal  is  to  search  through  the  whole  world 
and  find  -.very  fact  of  a  given  sort,  \ve  usually  know  perfectly 


DIFFERENCE    IN    CERTAINTY.  227 

well  that  the  search  has  been  incomplete,  and  even  when  we 
have  tried  to  make  it  complete  there  is  always  the  chance 
that  something  has  been  overlooked  and  that  we  really  have 
not  exhausted  the  universe  after  all.  This  is  why  the  induc- 
tive sciences  are  being  continually  corrected,  while  such  a 
science  as  geometry  (which  does  not  demand  this  exhaustive 
search  through  the  world)  stands  from  the  first  with  little  or 
no  correction.  Assume  the  uniformity  of  nature,  and  a 
'  perfect  induction  ',  or  one  which  really  exhausted  the  uni- 
verse in  question,  would  give  quite  as  much  certainty  as  de- 
duction ;  but  in  this  complex  world  of  which  we  are  so 
ignorant,  perfect  induction  is  little  more  than  an  ideal.  We 
come  as  near  to  it  as  we  conveniently  can  and  then  begin  to 
guess,  trusting  to  future  experience  to  correct  us  if  the  guess 
is  wrong.  But  the  fact  that  in  induction  we  often  have  to 
guess  for  lack  of  premises  or  for  lack  of  skill  to  put  them 
together  does  not  prove  that  if  anybody  had  the  premises  and 
had  the  skill  his  inductive  construction  of  facts  would  be 
any  less  infallible  than  his  deductive. 


CHAPTER    XXII. 
THE   UNIFORMITY   OF   NATURE. 

ACCORDING  to  the  old  definition,  "  Man  is  a  rational  ani- 
mal ";  and  to  say  this  means  much  more  than  merely  to  say 
he  is  rational.  Animals  are  distinguished  from  sticks  and 
How  we  stones  by  the  fact  that  they  can  feel  and  move, 

believe  in  it.  The  movement  comes  in  response  to  the  feeling; 
but  animals  differ  from  each  other  with  respect  to  the  con- 
nection between  the  two.  With  some  the  movement  follows 
upon  the  feeling  directly,  uniformly,  and,  so  far  as  we  can 
judge,  inevitably.  Others  can  postpone  the  movement  until 
they  have  stopped  and  considered.  Man  can  stop  longer 
and  consider  more  than  any  other  animal,  and  for  that  reason 
he  is  called  pre-eminently  rational.  But  even  man  cannot 
always  stop  and  consider  how  to  act  in  response  to  his  im- 
pressions. He  cannot  help  swallowing  anything  which  has 
begun  to  go  down  his  throat ;  he  cannot  endure  more  than  a 
certain  amount  of  pain  without  crying  out  ;  and  without  con- 
siderable training  he  cannot  avoid  raising  his  arms,  shutting 
his  eyes,  or  drawing  his  head  back  when  a  blow  is  aimed  at  his 
face.  Reflex  acts  like  these  shade  so  imperceptibly  into  the 
acts  which  we  call  purely  voluntary  that  it  is  often  impossi- 
ble to  say  whether  some  act,  even  if  it  is  our  own,  belongs  to 
the  one  class  or  to  the  other.  Moreover,  there  is  good  rea- 
son to  believe  that  all  voluntary  acts  are  built  up  on  a  basis 

228 


HOW  WE   COME   TO   BELIEVE  IN   IT.  229 

of  those  which  are  purely  reflex  and  instinctive  ;  so  that  if  we 
did  not  resemble  the  lower  animals  in  performing  the  latter 
we  should  never  be  capable  of  the  former  ;  and  if  this  were 
the  case — if  we  could  not  perform  a  voluntary  net — there 
would  be  no  use  in  considering  what  act  would  be  best. 
This  means  there  would  be  no  use  in  reasoning  ;  for  sooner 
or  later  all  reasoning  in  this  world  has  reference  to  some 
possible  act.  Therefore,  as  man  is  actually  constituted,  his 
being  rational  is  connected  in  the  closest  possible  way  with 
being  an  animal,  subject  to  all  sorts  of  impressions  from  the 
world  outside,  and  bound  to  respond  sooner  or  later  to  these 
impressions  by  some  kind  of  action. 

The  advantage  which  man  possesses  of  being  able  to  stop 
and  consider  how  to  act  longer  than  any  of  the  other  animals 
is  not  without  its  dangers.  To  let  an  opportunity  for  action 
go  by  is  often  quite  as  fatal  as  to  act  rather  stupidly.  A  fox 
that  considered  too  long  because  he  feared  a  trap  would  soon 
starve  to  death,  and  a  man  who  never  did  anything  until  it 
was  too  late  would  get  along  as  badly  as  one  who  acted  on 
every  impulse  as  soon  as  it  arose.  What  we  need  is  some 
way  of  combining  the  advantages  of  both  kinds  of  action, 
the  wisdom  of  the  deliberate  with  the  rapidity  of  the  purely 
reflex  or  impulsive ;  and  this  we  get  in  a  large  measure 
through  our  capacity  for  forming  habits.  When  an  act  has 
been  advantageous  we  tend  to  do  it  again  under  similar  cir- 
cumstances, and  every  time  we  repeat  it  it  becomes  more 
spontaneous,  easy  and  rapid,  until  at  last  it  becomes  to  all 
intents  and  purposes  purely  instinctive  or  reflex.  These 
results  of  habit  are  very  useful  in  the  main.  Of  course  habit 
has  its  drawbacks  as  well  as  its  advantages  ;  for  occasionally 
we  form  habits  that  are  bad  from  the  beginning,  and  some- 
times an  exceptional  condition  of  things  will  make  a  mode 
of  action  which  is  generally  good  extremely  inappropriate. 
But  the  race  would  not  have  acquired  and  kept  the  habit- 
forming  tendency  at  all  except  in  adjustment  to  a  world  in 
which  there  is  uniformity  enough  to  make  it  profitable. 


230  THE   UNIFORMITY   OF   NATURE. 

Mental  anticipations  are  one  form  of  habit.  These  do 
not  seem  to  come  at  first  in  the  form  of  anything  so  definite 
as  a  judgment.  The  new-born  child  does  not  say  '  Now  I 
shall  see  this  or  feel  that '.  He  does  not  ask  '  Is  it  to 
be  so  or  is  it  not  ? '  and  then  answer  his  own  question 
in  the  affirmative.  There  is  no  antithesis  between  '  Yes  ' 
and  '  No  '.  There  is  only  a  purely  reflex  expectation.  The 
image  of  the  anticipated  experience  enters  the  mind  and 
fills  it.  But  the  anticipation  comes  nevertheless,  and  thus 
in  the  imagination,  as  in  the  muscles,  the  nervous  system 
produces  a  very  na'ive  and  elementary  form  of  expectation. 
This  expectation  when  it  arises  is  not,  as  some  philosophers 
used  to  think,  derived  from  any  '  innate  principle  '  or  '  im- 
plicit '  or  '  unconscious '  thought  that  nature  is  always 
uniform;  but  in  each  particular  case  the  particular  expecta- 
tion arises  spontaneously  and  mechanically  as  a  result  of 
habit. 

All  this  is  only  to  say  that  man  is  a  creature  of  habit 
because  he  has  to  live  in  a  world  in  which  Nature  is  uniform. 
It  does  not  tell  how  we  came  to  believe  in  that  uniformity. 
The  blind  tendency  to  form  habits  and  thus  act  as  though 
order  were  to  be  expected  in  the  world  is  something  very 
different  from  the  explicit  thought  that  it  exists;  and  yet 
without  the  former  it  is  difficult  to  see  how  we  could  have 
gained  the  latter.  The  process  by  which  the  one  leads  to 
the  other  is  something  like  the  following. 

As  the  child  gets  along  in  life  and  his  expectations  are 
sometimes  disappointed  he  gains  a  sense  of  the  difference 
between  the  images  and  expectations  that  arise  from  within 
and  the  experiences  that  come  from  without,  i.e. ,  between 
thoughts  and  realities;  and  at  the  same  time  he  gains  a  sense 
of  the  difference  between  the  thoughts  that  correspond  to  the 
realities  and  those  that  do  not;  i.e.,  between  the  true  which 
he  can  welcome  with  the  judgment  '  Yes,  it  is  so  '  and  the 
false  that  he  must  reject  with  the  judgment  '  No,  it  is  not 
so  '.  Some  of  his  expectations,  however,  are  neither  grati- 


HOW   WE   COME   TO   BELIEVE   IN   IT.  231 

fied  immediately  nor  finally  disappointed,  but  only  delayed. 
If  he  smells  something  good  to  eat  he  may  have  to  wait 
before  he  can  get  it  or  even  see  it.  But  everything  that  he 
does  in  the  interval  is  done  with  the  anticipated  experience 
in  mind,  and  thus  his  activity  takes  the  form  of  a  search. 

Thus  a  period  of  delay  between  two  connected  experi- 
ences produces  a  modification  in  the  original  association. 
It  is  now  no  longer  a  matter  of  smell  and  sight  or  taste,  but 
of  smell,  expectation  and  search,  and  then  sight  or  taste. 
Moreover,  the  period  of  .expectation  and  search  is  sometimes 
longer  and  sometimes  shorter,  and  consequently  if  the  child 
had  to  go  away  some  day  without  finding  the  object  of  his 
search  he  would  still  think  of  it  as  there  and  picture  himself 
finding  it  at  the  end  of  a  longer  search;  so  that  at  last  he 
might  say  to  himself,  '  When  you  get  the  smell  (or  other 
sign,  whatever  it  is)  you  can  always  find  the  object  if  you 
look  long  enough  '.  In  some  such  way  as  this  we  come  to 
believe  that  a  uniform  connection  between  two  given  cir- 
cumstances exists  whether  we  happen  to  observe  it  or  not. 
The  same  sort  of  experience  taking  place  in  a  thousand  other 
relations,  we  learn  with  each  one  of  them  to  look  for  the 
circumstance  that  is  necessary  to  fulfil  our  spontaneous 
expectations,  or,  in  other  words,  to  look  for  the  relations  of 
things  necessary  to  make  our  experience  of  the  world 
uniform. 

In  cases  where  our  expectations  are  not  only  delayed  but 
positively  disappointed,  the  disappointment  or  surprise  is 
apt  to  prick  our  attention  and  make  us  notice  the  presence 
of  some  variation  in  the  conditions  that  we  had  not  observed 
at  first;  and  if  this  circumstance  happens  to  be  connected  in 
any  real  way  with  our  disappointment  and  the  experience 
is  repeated,  we  soon  learn  to  modify  our  expectations  and 
to  say  '  When  A  is  present  expect  B,  except  when  C  is  present 
also  '.  In  this  way  our  expectations  of  uniformity  become 
more  and  more  refined.  Moreover,  since  the  feeling  of  sur- 
prise is  present  in  every  case  of  disappointed  expectations,  if 


232  THE   UNIFORMITY   OF   NATURE. 

the  feeling  once  makes  us  open  our  eyes  and  look  around 
for  the  relation  necessary  to  make  our  experience  uniform  and 
if  the  search  proves  useful,  we  shall  be  more  likely  to  look 
around  the  next  time  we  are  surprised ;  and  thus  form  the 
general  habit  of  seeking  for  uniformities  when  they  are  not 
apparent. 

Even  this  habit  of  seeking  for  uniformities  in  all  the  situa- 
tions in  which  we  are  placed  is  something  different  from  a 
formal  conviction  that  Nature  is  always  uniform,  just  as  the 
habit  of  meeting  one's  obligations  is  different  from  any 
theory  that  he  should  be  honest;  but  for  practical  purposes 
the  habit  without  the  theory  is  better  than  the  theory  without 
the  habit.  The  habit  alone  is  sufficient  to  give  the  practical 
confidence  in  uniformity  with  which  induction  starts.  When 
the  logician  asks  the  man  of  sound  sense  and  practical  use- 
fulness what  reason  he  has  for  believing  that  the  uniformity 
he  looks  for  is  always  present  the  answer  will  probably  not 
satisfy  the  logician.  The  man  has  never  tried  to  give  his 
habit  of  thought  a  logical  basis;  perhaps  he  has  hardly 
recognized  that  he  had  it.  It  was  merely  one  of  the  uncon- 
scious products  of  his  nature  that  happened  to  help  keep 
him  alive.  Yet,  after  all,  when  the  general  truth  that  Nature 
is  always  uniform  does  dawn  upon  us  and  does  become 
explicitly  recognized,  it  is  through  the  habit.  For  if  the 
question  of  the  uniformity  of  Nature  is  ever  put  to  us  in  this 
general  way,  we  try  to  think  of  some  situation  in  which  we 
should  not  or  could  not  feel  the  impulse  to  seek  uniformity 
whether  we  actually  found  it  or  not,  and  when  we  cannot 
think  of  any  we  agree  that  uniformity  is  always  to  be  sought; 
and  this  implies  that  it  always  exists. 

There  is  nothing  in  the  world  but  a  vast  number  of  things 
of  various  kinds  acting  upon  each  other  in  various  ways 

under    various    circumstances,    and    we    cannot 
Its  two  .  , 

main  possibly  conceive   of  an   event  winch   could   not 

be  explained,  if  we  knew  enough  about  it,  as  due 
to   the  action  of  a  thing  or  things  of  some  particular  kind 


ITS   TWO   MAIN   ASPECTS.  233 

under  some  particular  kind  of  circumstance.  This  is  only 
another  way  of  saying  that  the  uniformities  we  expect  to  find 
in  the  world  take  two  main  aspects,  one  of  which  .is  indicated 
by  the  term  '  thing  '  and  the  other  by  the  term  '  circum- 
stance '. 

This  distinction  we  make  between  things  and  circumstances 
enables  us  to  find  uniformity  in  phenomena  even  when  they 
are  not  precisely  alike.  If  the  same  series  of  phenomena 
should  persist  or  recur  with  absolutely  no  variation,  like  the 
notes  in  a  piece  of  music  reeled  off  by  a  machine,  the  dis- 
tinction between  things  and  circumstances  would  not  be 
necessary;  each  part  would  be  determined  in  every  respect 
by  its  relation  to  the  inflexible  whole,  and  there  would  be 
no  other  particular  part  to  which  it  bore  any  special  relation. 
But,  as  our  experience  actually  occurs,  this  is  not  the  case. 
Experience  is  capable  of  infinite  variation,  and  still  it  can  be 
reduced  to  uniformity  of  the  sort  that  we  believe  in  by  dis- 
tinguishing between  these  two  aspects,  the  thing-aspect  and 
the  circumstance-aspect,  and  by  supposing  that  either  the 
thing  or  the  circumstance  can  be  changed  while  the  other 
remains  the  same,  or  that  both  can  be  changed  or  remain 
the  same  together.  In  this  way  our  belief  in  uniformity  does 
not  require  us  to  expect  an  absolute  repetition  of  events 
except  when  things  and  circumstances  are  both  the  same. 

To  explain  first  of  all  what  we  mean  by  the  thing-aspect 
of  uniformity.  We  distinguish  between  different  things,  and 
therefore  this  thing-aspect  of  uniformity  does  not  mean  that 
all  things  are  alike.  For  if  everything  in  the  world  were  to 
appear  and  act  precisely  like  everything  else  no  one  would 
be  able  to  distinguish  his  hat  from  the  cat  or  a  bar  of  soap, 
and  there  would  be  no  reason  why  he  should.  On  the  other 
hand,  if  everything  in  the  world  were  not  only  to  appear 
different  and  act  differently  from  everything  else,  but  were 
also  to  be  continually  changing  its  appearance  and  mode  of 
acting  in  a  perfectly  arbitrary  way,  it  would  still  be  impossi- 
ble to  distinguish  between  one  thing  and  another,  for  the 


234  THE   UNIFORMITY   OF   NATURE. 

points  of  difference  found  at  one  moment  would  cease  to 
exist  in  the  next.  In  the  first  case  any  expectation  would 
be  fulfilled  by  one  thing  as  well  as  by  any  other;  in  this 
latter  case  no  expectation  would  be  fulfilled  by  anything. 
Thus  while  the  possibility  of  distinguishing  between  things 
implies  that  they  differ  from  each  other,  it  also  implies  that 
each  of  the  things  distinguished  has  some  characteristic 
uniformity  of  appearance  or  way  of  acting  which  marks  or 
constitutes  its  own  individuality  or  nature. 

An  oxygen  atom  acts  in  one  way  in  the  presence  of 
hydrogen  and  in  another  in  the  presence  of  nitrogen,  but  it 
never  ceases  to  act  like  oxygen  and  begins  to  act  like  iron 
or  chlorine.  A  formula  which  told  the  various  ways  in  which 
it  does  act  under  all  possible  circumstances  would  be  a 
definition  of  its  nature. 

We  not  only  assume  that  every  thing  has  a  nature  of  its 
own,  but  we  assume  also  that  there  are  absolute  similarities 
between  them,  so  that  they  can  be  divided  into  various 
'  kinds  ',  all  the  things  of  a  given  kind  having  so  much  the 
same  '  nature  '  that  one  might  be  substituted  f  )r  another 
without  producing  any  perceptible  change  in  the  result. 

Along  with  the  uniformities  characteristic  of  certain  indi- 
viduals and  classes  of  things  we  come  to  have  also  some  idea 
of  the  uniformities  characteristic  of  things  in  general,  partic- 
ularly of  material  things.  A  material  thing,  as  contrasted 
with  a  mere  phantasm,  is  expected  to  be  tangible,  to  resist 
pressure  more  or  less,  to  have  a  continuous  existence  in  time 
and  space  in  the  sense  of  not  passing  from  one  point  to 
another  without  passing  through  all  the  intermediate  points; 
and  perhaps  also  to  obey  the  laws  of  inertia  and  gravitation. 
Finally,  since  things  are  only  given  as  aspects  of  the  sum 
total  of  experience  called  the  world  as  a  whole,  by  reference 
to  which  aspects  the  essential  uniformity  of  the  whole  can 
be  conceived,  it  is  a  part  of  the  very  nature  of  a  thing  to  be 
bound  up  with  others  in  a  whole  world,  to  act  upon  them 
and  to  be  acted  upon  by  them,  and  to  observe  the  same 


ITS   TWO   MAIN   ASPECTS.  235 

general  laws.  To  speak  of  a  thing  out  of  all  relations  to 
everything  else  is  to  speak  of  an  aspect  apart  from  that  whose 
aspect  it  is,  and  is  therefore  absurd. 

By  the  Circumstances  of  a  thing  as  contrasted  with  its 
nature  we  mean,  not  the  general  rule  of  its  action,  but  the 
particular  conditions  to  which  the  rule  must  be  adapted  at 
any  given  instant.  These  conditions  include  the  present  or 
vanishing  state  or  activity  of  the  thing  itself.  An  iron,  for 
example,  that  has  just  been  heated  will  not  act  precisely  like 
one  that  has  not.  They  include  also  the  position  and 
nature,  and  present  or  vanishing  states  or  acts,  of  other  things. 
Oxygen  does  not  act  in  the  presence  of  hydrogen  precisely 
as  it  acts  in  a  vacuum,  and  it  does  not  act  in  the  presence 
of  hot  hydrogen  precisely  as  it  does  in  the  presence  of  cold. 

When  I  say  that  the  conditions  which  help  to  determine 
an  act  include  the  position  and  state  of  other  things  besides 
the  agent,  I  mean,  not  merely  that  sometimes  an  act  is 
determined  in  part  by  something  outside  of  the  agent,  but 
that  it  is  always.  The  moth  in  its  chrysalis  seems  to  develop 
wholly  from  within,  shut  off  from  all  the  rest  of  the  world; 
but  take  away  the  warmth  of  the  sun  outside  and  how  long 
would  the  development  last  ?  Even  within  the  chrysalis  we 
have  not  one  simple  thing  moving  by  a  wholly  inward  law 
from  one  state  to  another,  as  we  may  be  inclined  to  assume 
at  first,  but  rather  a  whole  system  of  cells  acting  and  re- 
acting upon  each  other;  and  each  one  of  these  cells  again 
is  composed  of  atoms,  all  acting  with  reference  to  what  lies 
beyond  them.  In  short,  all  explanations  in  natural  science 
come  down  finally  to  atoms;  and  no  explanation  assumes 
that  an  atom  ever  acts  wholly  from  within,  regardless  of  the 
rest  of  the  world.  Therefore  every  ultimate  explanation  is 
made  on  the  assumption  that  every  act  or  state  of  a  thing  is 
determined  partly  from  without.  In  other  words,  causation 
always  involves  interaction.* 

*  This  is   quite  as   true  in  psychology  as  it  is  in  physical  science. 
When  we  '  explain  '  a  person's  thought  we  either  regard  it  as  due  to  the 


236  THE   UNIFORMITY   OF   NATURE. 

Circumstances,  like  things,  can  be  divided  into  various 
'  kinds  ' ;  but  in  their  case  the  division  is  always  rather  loose. 
Two  things  can  be  absolutely  alike  in  their  nature,  for  there 
is  no  reason  why  they  cannot  both  act  according  to  precisely 
the  same  general  law.  But  two  circumstances  can  never  be 
precisely  alike.  If  one  exists  here  at  this  time  the  other  must 
exist  somewhere  else  or  at  some  other  time,  and  conse- 
quently they  must  always  differ  in  time  or  place  if  in  nothing 
else.*  We  often  speak  of  two  circumstances  being  exactly 
alike,  but  when  we  do  so  we  only  mean  that  they  are  alike 
in  every  respect  that  is  worth  considering  for  the  purpose  in 
hand.  Circumstances  of  essentially  the  same  kind,  like 
things  of  the  same  kind,  can  be  substituted  for  each  other 
without  any  essential  change  in  the  resulting  phenomena. 
If  they  could  not,  the  division  of  experience  into  the  two 
aspects  of  things  and  circumstances  would  not  help  us  in  our 
conception  of  its  uniformity.  Wind  blowing  upon  the  green 
leaves  of  an  aspen-tree  here  to-day  makes  them  move  here 
and  to-day,  if  every  other  circumstance  is  the  same,  just  as 
wind  blowing  upon  them  there  and  yesterday  made  them 
move  there  and  yesterday. 

play  of  different  feelings  and  ideas  or  else  we  turn  to  physiology  and 
regard  it  as  due  to  various  '  currents  '  in  the  cells  and  fibres  of  the  brain. 
In  either  case  the  explanation  involves  something  beyond  what  is  ex- 
plained. Of  course  this  causal  analysis  does  not  prevent  us  from  believ- 
ing in  the  real  unity  of  the  mind,  and  a  similar  analysis  in  natural  sci- 
ence does  not  prevent  us  from  believing  in  the  unity  of  the  world.  The 
fact  that  explanations  take  account  of  aspects  of  reality  does  not  turn 
these  aspects  into  something  independent  and  self-existent. 

*  I  do  not  refer  to  their  absolute  position  in  time  and  space, —to  mere 
position  apart  altogether  from  the  relation  of  events  to  other  events  that 
precede  or  coexist  with  them  and  of  things  to  other  things  that  surround 
them.  Such  absolute  position  does  not  enter  into  our  explanations  at 
all,  and  is  therefore  not  a  'circumstance'  in  the  sense  in  which  the  word 
is  used  here.  When  we  say  that  the  result  of  an  act  was  different  in  two 
different  cases  because  the  act  occurred  at  two  different  times  it  is  not 
the  bare  time  as  such  that  we  have  in  mind,  but  the  preceding  or  con- 
current events;  and  the  same  is  true,  mutatis  mutandis,  oi  differences  in 
place. 


LAW.  237 

Having  divided  our  world  into  these  two  aspects  of  thing 
and  circumstance  we  are  not  satisfied  to  say  merely  that 
under  precisely  similar  circumstances  precisely 
similar  things  will  produce  precisely  similar 
results.  We  go  further,  and  seek  for  laws,  which  take 
account  of  the  differences  between  things  and  circumstances 
as  well  as  of  their  resemblances,  and  which  tell  not  merely 
what  takes  place  when  the  same  things  or  precisely  similar 
things  are  placed  in  precisely  similar  circumstances,  but  tell 
also  how  much  variation  in  the  circumstances  or  the  things 
produces  a  given  amount  of  variation  in  the  result.  We  do 
not  merely  say  that  bodies  attract  each  other;  but  we  say 
that  they  attract  each  other  in  direct  proportion  to  their  mass 
and  in  inverse  proportion  to  the  square  of  their  distance. 
This  would  not  be  possible  unless  we  took  account  of  the 
amount  of  difference  between  two  situations  and  measured 
off  one  against  another.  It  is  this  recognition  of  differences 
in  amounts  of  difference,  and  their  precise  measurement, 
that  enables  us  to  introduce  the  conception  of  proportion 
into  our  formulas  and  to  deal  with  them  by  mathematics. 

The  notion  of  law  would  be  impossible  and  our  search 
for  uniformity  in  the  world  would  be  doomed  to  failure  if 
our  ability  to  see  different  aspects  of  reality  were  limited  to 
the  general  distinction  between  things  and  circumstances. 
But  the  very  ability  to  enumerate  a  thing's  different  attri- 
butes involves  the  power  on  our  part  of  attending  to  one  of 
them  at  a  time,  and  in  the  same  way  the  very  possibility  of 
stating  some  general  law  such  as  that  of  gravitation  involves 
the  power  of  attending  to  some  one  of  a  thing's  relations 
and  accounting  for  it  without  saying  anything  about  the  rest. 
In  accounting  for  the  fall  of  an  apple  by  this  law,  we  con- 
sider its  mass  and  the  mass  of  the  earth,  its  motion  towards 
the  earth,  and  the  original  distance  between  them.  We  do 
not  say  anything  about  its  taste  or  color  or  even  perhaps 
about  its  size  and  shape  and  its  motion  around  the  sun.  Of 
course  these  neglected  relations  must  be  accounted  for  too, 


238  THE   UNIFORMITY   OF   NATURE. 

and  the  state  of  affairs  that  produces  them  must  be  compati- 
ble with  the  state  of  affairs  that  produces  the  apple's  fall. 
The  total  state  of  the  world  at  every  instant  is  the  cause  of 
its  total  state  at  the  next;  but  we  feel  that  we  have  a  right 
in  our  explanations  to  break  up  this  complex  whole  of  each 
instant  into  as  many  aspects  or  different  relations  as  we 
please  and  account  for  some  of  them  at  a  time. 

Thus  the  uniformity  discovered  by  each  one  of  our  explana- 
tions is  a  uniformity  in  some  one  definite  respect,  and  when 
we  speak  of  the  '  Cause  '  of  an  event  we  are  almost  always 
trying  to  pick  out  the  essential  elements  of  its  nature  and 
the  relations  to  its  own  past  and  to  other  things  that  account 
for  some  few  of  its  salient  features.  Nothing  short  of  the 
whole  universe  would  account  for  the  event  as  an  absolutely 
complete  whole. 

The  ability  of  which  we  have  just  spoken  to  attend  to 
some  one  aspect  of  a  situation  involves  certain  dangers. 

For  we  may  forget  that  the  situation  has  other 
Precision  ,  .  .  .  . 

in  aspects  which  might  also  be  accounted  for,  and 

therefore  rest  with  the  feeling  that  our  explana- 
tion of  the  situation  as  a  whole  is  complete  when  it  is  really 
very  incomplete.  Worse  still,  the  explanation  which  we  give 
of  the  aspect  of  the  situation  that  we  happened  to  notice 
may  be  quite  inconsistent  with  any  reasonable  explanation 
of  the  other  aspects  that  we  did  not  happen  to  notice,  and 
therefore  wrong,  without  our  detecting  the  fact,  as  we  should 
have  done  if  we  had  realized  how  much  there  was  to  explain. 
We  may  say  that  the  light  on  the  wall  comes  through  a 
certain  window,  and  be  perfectly  satisfied  with  the  explana- 
tion so  long  as  we  fail  to  notice  that  the  glass  in  the  window 
is  blue  and  the  light  on  the  wall  is  not. 

Nay,  even  if  we  notice  such  a  discrepancy,  we  may  delib- 
erately disregard  it,  with  the  feeling  that  in  some  way  or  other 
it  can  be  detached  from  the  rest  of  the  phenomenon,  and 
therefore  makes  no  difference,  and  that  in  any  case  it  must 
not  be  allowed  to  interfere  with  the  conclusion  already 


PRECISION   IN   UNIFORMITY.  239 

reached.  This  is  more  likely  to  be  true  when  our  emotions 
are  involved.  If  a  storekeeper  has  been  robbed  and  there 
are  five  or  six  impressive  circumstances  which  all  suggest  a 
certain  clerk  as  the  culprit,  he  may  jump  to  the  conclusion 
that  the  clerk  is  guilty,  although  he  is  perfectly  aware  of 
some  other  circumstance,  which  is  less  striking,  but  which 
is  nevertheless  absolutely  incompatible  with  the  clerk's  guilt. 
If  this  circumstance  is  mentioned  and  the  storekeeper  is 
forced  by  it  to  admit  that  the  clerk  is  not  guilty  there  is 
considerable  chance  that  he  will  admit  it  very  reluctantly, 
and  will  still  feel  that  he  'nearly  did  it',  and  bear  him  a 
grudge  accordingly.  The  good  reasoner,  whether  he  be  a 
scout  finding  a  trail,  a  detective  tracing  a  crime,  a  physician 
diagnosing  a  case,  or  a  scientist  pure  and  simple,  is  the  one 
who  has  not  only  skill  enough  to  observe  the  less  striking 
circumstance  but  strength  enough  to  hold  it  in  mind  until  it 
is  accounted  for,  instead  of  allowing  it  to  be  swept  away  like 
the  still  small  voice  of  conscience  by  the  larger  mass  of  more 
vigorous  impressions  and  associations  that  hurry  us  on  to  a 
more  apparent  goal. 

•  Even  in  the  aspect  of  a  situation  that  we  really  do  attend 
to  we  may  overlook  the  necessity  for  explaining  the  finer 
details.  Every  one  knows  in  a  general  way  that  rough  water 
is  caused  by  wind;  but  when  we  have  accounted  for  this 
general  appearance  of  roughness  most  of  us  are  satisfied. 
As  Professor  Huxley  says:  "Even  thoughtful  men  receive 
with  surprise  the  suggestion"  that  the  form  of  every  wave 
and  the  direction  taken  by  every  particle  of  foam  "  are  the 
exact  effects  of  definite  causes  ";  and  so  long  as  we  fail  to 
recognize  this  precision  of  the  causal  relation  it  is  perfectly 
evident  that  we  do  not  realize  the  complete  uniformity  of 
nature. 

Thus  while  it  is  absolutely  necessary  that  we  should  ignore 
certain  aspects  of  a  situation  when  we  try  to  explain  others, 
it  is  quite  as  necessary  that  we  should  not  ignore  the  wrong 
ones.  The  only  thing  to  do  under  these  circumstances  is 


240  THE   UNIFORMITY   OF   NATURE. 

first  to  make  an  explanation  that  will  account  for  the  aspect 
of  the  situation  in  which  we  are  interested  and  then  to 
inquire  in  a  cold-blooded,  critical  way  whether  there  are  not 
other  aspects  of  the  situation  with  which  the  explanation  is 
not  consistent.  If  there  are  we  must  reject  it  even  though 
it  has  cost  us  years  of  labor.  It  may  be  that  every  one  has 
a  lurking  tendency  to  feel  that  a  plausible  explanation  has 
some  value,  whether  it  be  true  or  not,  until  it  is  proved  to 
be  false.  But — except  as  it  helps  us  to  remember  the  facts 
themselves — it  has  not,  and  the  sooner  we  recognize  its 
falseness  and  try  to  find  one  that  will  stand  in  spite  of  criti- 
cism, the  better  it  is  for  ourselves  and  everybody  else.  It  is 
useless  to  try  and  live  in  a  fool's  paradise  or  to  bury  our 
heads  in  the  sand  and  refuse  to  recognize  the  disagreeable 
facts  that  upset  our  theories. 

Besides  the  necessity  for  looking  at  one  aspect  of  a  situa- 
tion at.  a  time  there  is  another  reason  why  it  is  hard  to  realize 
that  every  event  "is  the  exact  effect  of  definite  causes"; 
namely,  because  it  is  hard  to  realize  that  the  events  them- 
selves are  exact  and  definite.  Most  of  our  ideas  are  very 
hazy,  and  it  takes  hard  training  to  make  us  realize  that  the 
realities  which  these  ideas  profess  to  represent  are  not  as 
hazy  as  the  ideas  themselves;  that  though  we  can  form  no 
clear  idea  of  the  beginning  of  things,  there  was  no  chaos,  no 
mere  'stuff'  without  definite  attributes  and  relations;  and 
that  though  we  may  be  in  doubt  about  some  state  of  affairs, 
there  is  no  uncertainty  or  hesitation  in  the  state  of  affairs 
itself.  Hazy  thoughts  claim  to  represent  reality  as  much  as 
clear  ones,  and  so  long  as  all  our  thoughts  are  hazy  we 
cannot  realize  that  the  claim  is  false.  We  must  know  some 
things  definitely  before  we  can  begin  to  realize  that  all  things 
are  definite  whether  we  know  them  definitely  or  not. 
Whenever  we  have  used  exact  measurements  so  often  that 
we  feel  the  tendency  to  apply  them  to  everything  and  no 
description  seems  complete  without  accurate  statements 
about  size,  shape,  direction,  number,  duration,  degree,  and 


THE   THING-ASPECT   OF   THIS   PRECISION.  241 

ao  on,  we  are  then  in  a  position  to  realize  that  these  quanti- 
tative relations  of  things  fit  into  the  general  law  of  uniformity 
as  well  as  the  qualitative.  Then,  but  hardly  any  sooner,  do 
we  realize  that  the  form  of  every  wave  and  the  path  of  every 
falling  leaf  are  '  the  exact  effects  of  definite  causes ' ;  that 
the  law  of  uniformity  is  not  only  universal  but  precise. 

To  realize  the  uniformity  of  nature  it  is  quite  as  necessary 
to  keep  a  clear  view  of  the  individuality  or  separateness  of 
different  things  as  to  make  clear  distinctions 
between  different  circumstances.  Yet  this  abso- 
lute  distinction  between  different  things  we  often 
tend  in  our  instinctive  reactions  to  ignore.  If 
we  are  stung  by  one  hornet  it  seems  appropriate  in  revenge 
to  wipe  out  the  entire  nestful,  whether  it  includes  the  one 
that  hurt  us  or  not.  If  certain  Americans  are  massacred  by 
a  set  of  Chinamen  in  Asia  it  is  perfectly  natural  for  a  mob 
of  other  Americans  to  revenge  itself  by  attacking  some  inno- 
cent laundryman  in  Kansas  City.  If  two  or  three  members 
of  a  household  do  us  an  injury  it  is  difficult,  especially  if  we 
are  not  brought  into  close  contact  with  them,  not  to  harbor 
resentment  against  the  whole  household.  To  the  individuals 
themselves  the  difference  between  them  may  mean  everything; 
to  us  it  means  nothing  at  all. 

In  much  the  same  way  as  we  ignore  the  numerical  differ- 
ence between  several  individuals  and  treat  one  as  though  in 
some  way  it  were  actually  identical  with  another  because  it 
belongs  to  the  same  group,  so  we  ignore  also  the  distinction 
between  different  kinds  of  individuals.  To  make  an  accurate 
definition  is  one  of  the  hardest  things  in  the  world;  but  the 
curious  thing  is  that  it  often  comes  to  people  as  a  sort  of 
revelation  that  such  definitions  can  be  made  at  all.  '  Defini- 
tion is  possible  !  '  This  thought  it  was,  perhaps  more  than 
any  other,  which  gave  Socrates  a  life-long  inspiration.  But 
to  assert  the  possibility  of  definition — to  say  that  some 
moral  attribute  or  some  material  thing  can  be  defined  in  such 
a  wav  as  to  include  by  the  verv  definition  all  that  we  think 


242  THE   UNIFORMITY   OF   NATURE. 

the  word  should  stand  for,  and  to  exclude  all  that  we  think 
it  should  not — is  only  another  way  of  saying  that  whether 
we  can  find  it  or  not  the  difference  between  things  or  kinds 
of  things  is  always  perfectly  definite. 

In  still  another  way  uniformity  of  nature  involves  more 
about  things  than  is  evident  at  first.  It  involves  the  abso- 
lute permanence  of  whatever  can  truly  be  called  a  Thing. 
People  often  suppose  that  when  things  are  '  burned  up  '  the 
total  amount  of  matter  or  of  ultimate  things  in  the  world  is 
diminished  and  that  when  plants  grow  it  is  increased.  But 
such  a  supposition  is  inconsistent  with  the  very  idea  of  a 
thing  and  with  all  our  explanations  of  events  that  involve  it. 
When  we  say  that  some  given  event  is  due  to  the  circum- 
stances in  which  certain  things  were  placed,  we  take  it  for 
granted  that  the  things  existed  before  the  circumstances,  and 
were  thus  at  least  relatively  permanent;  and  when  we  learn 
that  the  permanence  of  sticks  and  stones  and  other  such 
things  by  which  we  have  explained  events  is  not  absolute, 
we  account  for  it  by  saying  that  after  all  they  are  not  really 
things  at  all  in  the  ultimate  sense  of  the  word,  but  only 
temporary  combinations  of  atoms,  which  latter  are  truly  per- 
manent ;  and  that  the5;e  atoms  are  the  true  things.  Thus 
we  come  to  realize  what  the  scientists  call  the  conservation 
of  matter.  The  permanence  of  things  is  one  of  the  two  great 
aspects  under  which  we  think  of  the  general  law  of  uni- 
formity in  the  world;  and  to  assume  that  any  real  thing  is 
not  permanent  is  therefore  to  deny  the  existence  of  absolute 
uniformity.  Yet  it  is  difficult  to  realize  in  a  positive  way 
that  the  law  of  uniformity  implies  the  absolute  permanence 
of  every  ultimate  '  thing '.  This  scientific  principle  of  the 
conservation  of  matter  (and  of  any  other  ultimate  reality) 
states  for  the  things  involved  the  same  absolute  uniformity 
that  the  law  of  absolutely  precise  causation  states  for  the 
circumstances  in  which  they  are  placed. 

Thus  far  we  have  explained  how  we  grow  into  the  belief 
that  Nature  is  uniform,  and  we  have  shown  the  forms  which 


PROOF  OF  UNIFORMITY.  243 

we  expect  that  uniformity  to  take;  and  yet  after  all  we  have 
not  proved  that  such  uniformity  exists,  and  it  is  the 
proof  of  facts  and  not  the  history  of  beliefs  with 
which  we  are  concerned  in  logic.  But  where  would  such  proof 
begin  ?  If  we  do  not  take  uniformity  of  any  sort  for  granted 
we  should  have  to  begin  like  Descartes  by  pretending  to  doubt 
our  own  existence  and  the  existence  of  other  people  to  whom 
the  proof  might  be  addressed,  for  even  personal  identity  is  a 
principle  of  uniformity;  and  we  should  assuredly  share  in 
Descartes'  failure.  If,  on  the  other  hand,  we  are  willing  to 
be  less  thoroughgoing  than  Descartes  and  take  something  for 
granted  to  begin  with,  and  thus  begin  our  attempted  demon- 
stration with  the  assumption  that  there  are  things  and  that 
various  uniformities  have  existed  in  the  past,  why  is  this 
any  evidence  that  other  kinds  of  uniformity  exist  now  or 
that  any  whatever  will  exist  in  the  future, — unless  we  already 
take  for  granted  some  wider  principle  of  uniformity  which 
decrees  that  if  uniformity  exists  anywhere  or  at  any  time  it 
must  exist  everywhere  and  always  ?  The  fact  that  the  sun 
has  risen  (as  we  believe)  every  twenty-four  hours  throughout 
long  ages  makes  us  expect  that  it  will  rise  to-morrow;  but 
unless  we  already  assume  that  the  future  will  resemble  the 
past  it  does  not  prove  it. 

Possibly  the  best  thing  that  any  one  can  say  in  justifica- 
tion of  his  conviction  that  experience  depends  upon  a  world 
of  uniform  relations  is  merely  this:  that  it  is  a  faith  growing 
out  of  his  very  nature  as  an  active  being  (if  he  exists  and 
has  a  nature),  that  he  has  lived  by  it  in  the  past  (if  he  has 
had  a  past),  that  the  longer  he  has  taken  it  for  granted  the 
more  it  has  seemed  to  justify  itself,  and  that  he  means  to 
take  it  for  granted  in  the  future  (if  there  is  a  future).  Our 
belief  in  the  uniformity  of  things  is  thus  something  which 
we  can  account  for  psychologically,  and  we  can  show  that 
to  deny  this  uniformity  in  toto  involves  conclusions  which  no 
sane  man  is  willing  to  act  upon  ;  but  there  is  no  direct  way 
of  proving  its  existence. 


CHAPTER   XXIII. 

SCIENCE  AND   THE    PECULIARITIES   OF    THE    RELATIONS 
THAT    IT   TRACES. 

THE  conviction  that  there  is  a  distinction  between  circum- 
stances and  things  is  only  a  starting-point  in  our  search  for 

the   uniformity   that   we  believe  to   pervade  the 
Twofold  .  ,        „,  ...... 

work  of  world.       1  he  vast  differences  between  one  corn- 

science.  .  ,     , 

plex  group  of  phenomena  and  another  are  not 

explained  to  our  satisfaction  by  the  mere  general  statement 
that  they  are  all  due  to  differences  between  things  and  the 
circumstances  in  which  they  are  placed.  The  difference 
between  one  complex  situation  and  another  is  always  per- 
fectly definite,  and  what  we  want  to  find  out  is  the  precise 
difference  in  the  things  and  in  the  circumstances  that 
accounts  for  this  definite  difference  in  the  situations  as  a 
whole.  This  is  the  business  of  Science,  and  its  work  has 
two  sides:  (i)  Observing  as  much  as  we  can,  and  finding 
out  from  what  we  observe  the  general  laws  according  to 
which  things  always  act;  and  (2)  inferring  further  from  the 
concrete  combination  of  circumstances  or  events  that  we 
observe  and  from  the  general  laws  that  we  have  discovered 
what  must  be  the  concrete  state  of  affairs  where  we  cannot, 
or  cannot  yet,  observe.  As  a  result  of  various  concrete 
observations  made  by  himself  and  others  Newton  discovered 
and  proved  the  law  of  gravitation;  and  an  astronomer  who 
knows  this  law  and  also  observes  the  position  of  some 
heavenly  body  at  various  intervals  is  able  to  tell  where  it  was 
before  he  saw  it,  when  it  will  come  within  a  certain  distance 

244 


INDIVIDUAL  IDENTITY   AND   CAUSATION.  245 

of  the  earth  or  the  sun,  and  what  will  happen  to  it  and  to 
them  when  it  does.  In  this  way  any  one  who  was  master 
of  an  absolutely  perfect  science  would  be  able  (i)  to  find 
every  law  in  the  universe,  and  then  (2)  starting  with  the 
present,  to  go  back  indefinitely  and  tell  the  history  of  the 
past  and  to  look  forward  just  as  far  and  tell  the  story  of  the 
future.  In  the  following  chapters  we  shall  speak  first  of  the 
logical  method  pursued  by  scientists  in  the  discovery  of 
general  laws,  and  afterwards  of  the  application  of  these  laws 
for  the  discovery  of  particular  concrete  facts.  But  before 
we  begin  it  is  desirable  to  say  a  few  words  more  about  the 
nature  of  the  identity  and  causal  interaction  assumed  in  all 
such  investigations. 

To  tell  whether  one  object  resembles  another  we  need  only 
look  at  the  two  and  compare  them,  and  in  the  same  way  we 
can  often  tell  by  direct  observation  whether  one 

event  succeeds  another:  but  to  tell  whether  one  Peculiarities 

.........  ,      ,  of  individual 

object  is  identical  with  another,  or  whether  some  identity 

.         .  ,  ,  .        .  and  causal 

given    event    is    the    cause    of   another,    simple  interaction. 

inspection  is  not  sufficient.  If  we  lose  sight  of 
a  thing  for  a  single  instant  how  can  we  tell  that  it  has  not 
been  removed  and  another  put  in  its  place  ?  Indeed,  until 
we  know  something  more  about  it  than  its  outward  appear- 
ance, how  can  we  even  be  sure  that  such  a  substitution  has 
not  taken  place  by  some  jugglery  before  our  very  eyes  ?  So 
also  with  the  causal  relation  between  one  thing  and  another; 
however  certain  we  may  be  that  a  change  we  observe  in  one 
thing  followed  immediately  after  a  change  we  observed  in 
something  else,  how  can  we  be  sure  that  it  was  caused  by 
this  rather  than  by  a  change  in  some  third  thing,  miles  away 
perhaps,  that  we  did  not  happen  to  observe  at  all  ?  No  one 
can  directly  observe  either  the  identity  of  an  object  with 
itself  or  its  causal  action  upon  something  else,  and  therefore 
our  identifications  and  causal  explanations  have  to  be  reached 
by  guesswork  in  the  first  instance,  and  if  they  are  afterwards 
proved  to  be  correct  the  proof  has  to  be  indirect. 


246         SCIENCE   AND   THE   RELATION   IT   TRACES. 

Another  thing  to  notice  about  these  relations  of  identity 
and  causal  interaction  is  the  conviction  we  feel  that  they  are 
always  present.  Since  they  are  aspects  of  the  uniformity  of 
nature  that  we  believe  in,  we  have  a  right  to  believe  that  at 
every  moment  in  the  past  there  were  things  identical  with 
the  things  of  the  present,  and  that  there  are  and  always  have 
been  causal  relations  to  other  things  that  help  to  explain 
their  present  conditions;  and  the  same  is  true,  mutaiis  mutan- 
dis, of  the  future. 

Still  another  peculiarity  of  these  two  relations  is  their 
exclusiveness.  In  this  respect  identity  and  causal  interaction 
are  very  different  from  resemblance  and  succession.  The 
house  I  live  in  can  be  similar  to  each  one  of  a  hundred 
others,  wholly  regardless  of  the  place  and  time  of  their  exist- 
ence, and  its  similarity  to  one  does  not  interfere  in  the 
slightest  with  its  similarity  to  some  other.  It  is  true  too 
that  the  house  that  keeps  out  the  rain  to-day  can  be  identical 
with  the  house  that  was  bathed  in  sunshine  yesterday  and 
none  the  less  identical  on  that  account  with  the  house  that 
was  covered  with  snow  two  months  ago,  for  these  relations 
of  identity  and  causation  go  back  from  instant  to  instant 
without  a  break  to  all  eternity;  but  the  house  cannot  be 
identical  with  one  existing  in  some  other  place  or  state  at 
the  same  time.  There  is  only  one  thing  at  a  time  with  which 
it  can  be  identical,  and  to  be  identical  with  this  means  not 
to  be  identical  with  some  other.  The  same  exclusiveness  is 
found  also  in  the  case  of  causation.  The  house  we  have 
been  talking  about  can  exist  at  the  same  time  as  an  unlimited 
number  of  others,  and  an  unlimited  number  of  things  might 
have  been  acting  before  or  during  its  erection;  but  if  the 
house  was  built  by  John  Smith  it  could  not  have  been  built 
by  anybody  else;  and  if  a  spark  from  a  certain  locomotive 
destroyed  it,  it  is  quite  certain  that  an  earthquake  or  a  stroke 
of  lightning  did  not.  It  is  perfectly  true,  to  be  sure,  that  if 
we  try  to  explain  absolutely  everything  about  the  house  as  it 
exists  at  a  given  instant  the  explanation  will  have  to  include 


INDIVIDUAL   IDENTITY   AND   CAUSATION.  247 

a  statement  about  absolutely  everything  in  the  universe  the 
instant  before.  Thus,  inasmuch  as  the  position  in  space  of 
every  object  depends  upon  that  of  every  other,  the  position 
of  the  house  would  certainly  be  affected  by  a  boy  throwing 
a  stone  in  China.  And  if  we  use  the  word  '  cause  '  with  refer- 
ence to  some  single  aspect  or  relation  of  things  that  we  are 
trying  to  explain  it  is  true  also  that  even  this  single  relation 
may  be  due  to  the  co-operation  of  several  causes.  John 
Smith  may  not  have  built  the  house  alone.  But  when  causes 
co-operate  in  this  way  no  one  of  them  is  a  complete  cause. 
If  anything  is  the  complete  cause  of  a  condition,  so  far  at 
least  as  one  instant  of  time  is  concerned,  it  is  its  sole  cause. 
A  resemblance  or  coexistence  or  succession  can  belong  at 
once  to  many  things  without  diminishing  the  share  of  any. 
A  relation  of  identity  or  causal  interaction  can  not. 

Our  knowledge,  or  rather  our  assumption,  that  these  rela- 
tions of  individual  identity  and  causal  interaction  always 
exist  and  are  always  exclusive  is  very  helpful  in  our  search 
for  uniformity  in  nature.  If  we  have  any  way  of  showing 
that  this,  that,  and  the  other  thing  of  one  instant  is  not 
identical  with  the  thing  of  another,  the  first  of  these  assump- 
tions gives  us  a  right  to  infer  that  some  other — perhaps  the 
only  one  left — is.  In  the  same  way,  if  we  have  any  means 
of  showing  that  this,  that,  and  the  other  thing  had  nothing 
to  do  with  some  present  condition  of  a  thing  that  we  are 
inquiring  about,  our  assumption  gives  us  the  right  to  infer 
that  something  else  had.  In  this  way  we  can  apply  the 
'  method  of  exhaustion  '  in  our  search  for  particular  uni- 
formities. So  with  the  second  assumption,  if  we  know  that 
this  thing  of  one  instant  is  identical  with  a  given  thing  of 
another,  we  know  perfectly  well  that  we  need  not  look  for 
any  other  thing  of  the  same  instant  to  be  identical  with  it. 
Here  again  the  same  is  true,  mutatis  mutandis,  of  causation. 
In  this  way  our  search  for  uniformity  is  simplified  and 
shortened. 

The  fact  that  causes  may  be  endlessly  complex  gives  one 


248         SCIENCE   AND   THE   RELATION   IT   TRACES. 

of  our  two  relations — that  of  causal  interaction — still  another 
peculiarity,  which  is  very  important.  The  relatively  simple 
relations  between  two  or  more  things  that  we  are  accustomed 
to  pick  out  arid  call  relations  of  cause  and  effect  are  not 
independent;  for  the  sequence  of  what  we  call  the  '  effect ' 
upon  what  we  call  the  'cause'  is  at  the  mercy  of  other 
causal  relations.  If  two  things  are  similar  their  similarity  is 
neither  increased  nor  diminished  by  their  likeness  to  other 
things  or  by  the  likeness  of  other  things  to  each  other.  John 
does  not  look  any  the  less  like  James  because  he  looks  like 
Henry  also,  or  because  Henry  looks  like  Thomas.  In  the 
same  way,  if  the  line  AB  meets  the  line  AC  at  an  angle  of 
45  degrees  you  can  draw  as  many  more  lines  as  you  like  to 
the  point  A  from  as  many  different  directions  as  you  like, 
without  affecting  the  size  of  the  angle  in  the  slightest.  As  a 
result  of  this  we  are  justified  in  absolutely  ignoring  the  exist- 
ence of  Henry  when  we  are  discussing  the  resemblance  of 
John  and  James,  and  in  ignoring  all  the  other  lines  which 
meet  at  A  when  discussing  the  relations  of  AB  and  AC. 

This  possibility  of  considering  two  relations  regardless  of 
everything  else  in  the  world  is  what  makes  the  problems  of 
deduction  and  of  geometry  so  relatively  simple.  But  with 
causation  all  this  is  changed.  John  can  beat  James  in  a 
fight  if  they  are  left  alone,  but  if  Thomas  warns  James  to  run 
or  takes  part  too  he  cannot;  the  sun  will  keep  a  comet  in  a 
certain  path  if  they  are  left  alone,  but  if  Jupiter  happens  to 
come  too  near,  the  comet  may  swing  out  of  its  path;  and 
so  on.  Whether  A  is  similar  to  B  is  a  mere  question  between 
A  and  B;  but  whether  A  will  cause  B  to  act  in  a  certain  way 
is  a  question  that  also  involves  C  and  D  and  E;  and  when 
we  are  trying  to  find  out  what  A  will  make  B  do  we  must 
know  whether  C  and  D  and  E  are  present  and  how  they  are 
acting.  We  cannot  ignore  them.  If  they  are  not  affecting 
the  relations  of  A  and  B  we  must  make  sure  that  they  are 
not;  and  this,  of  course,  makes  our  problem  much  more 
complex.  Deduction  and  geometry  can  neglect  irrelevant 


INDIVIDUAL  IDENTITY   AND   CAUSATION.  249 

circumstances;  inductive  reasoning  about  relations  of  cause 
and  effect  must  eliminate  them.  This  is  often  very  difficult; 
and  when  the  elimination  has  been  made  and  we  are  thus 
able  to  conclude  from  the  cases  examined  that  A's  action 
was  the  cause  of  B's,  we  must  not  conclude  from  this  that 
this  same  act  on  A's  part  will  always  be  followed  by  the 
same  act  on  E's;  but  only  that  such  will  always  be  the  case 
as  long  as  nothing  else  interferes.* 

This  fact  that  one  cause  can  interfere  with  another  is  what 
makes  a  knowledge  of  causal  relations  so  very  important 
practically  as  well  as  theoretically.  No  human  effort  can 
change  a  thing's  identity,  but  if  we  know  enough  we  can 
use  our  bodies  in  such  a  way  as  to  pit  one  cause  in  the  world 
against  another  and  change  its  effects  in  accordance  with 
our  purposes.  This  is  why  knowledge  is  power.  The  thing 
that  makes  the  knowledge  of  causal  relations  most  difficult 
is  the  very  thing  that  makes  it  useful. 

*  In  this  connection  the  reader  may  recall  the  statement  made  on  p.  80 
that  causal  relations  seem  to  penetrate  into  the  very  being  of  things, 
while  non-dynamic  relations  exist  only  externally  for  some  observer.  In 
this  respect  identity  is  like  causation. 


CHAPTER   XXIV. 

THE   METHOD   OF   EXHAUSTION   AND   THE   SEARCH     FOR 
PARTICULAR  UNIFORMITIES. 

WE  use  the  method  of  exhaustion  when  we  base  a  conclu- 
sion upon  the  results  of  a  more  or  less  direct  and  serious 
attempt  to  examine  every  case  of  a  given  sort  in  the  universe. 

The  simplest  application  of  this  principle  is  found  in  the 
so-called  Aristotelian,  or  Perfect,  Induction.  The  first  ex- 
ample of  induction  given  on  page  224  was  of  thii 
induction.'  sort,  namely:  This,  that,  and  the  other  member 
of  a  certain  family  each  has  light  hair;  these 
members  constitute  the  whole  family ;  therefore  every  mem- 
ber of  the  family  has  light  hair.  In  the  same  way  we  can 
sav :  '  The  apostle  James  was  a  Jew ;  so  was  John ;  so  was 
Peter  ' ;  and  so  on  through  the  twelve;  '  therefore  the  twelve 
apostles  were  all  Jews  '.  January  contains  less  than  thirty- 
two  davs;  so  do  February,  March,  etc.;  therefore  each 
month  of  the  year  contains  less  than  thirty-two  days.  In 
this  '  perfect  induction  '  the  conclusion  is  something  more 
than  a  mere  summary  of  the  particular  facts  stated  in  the 
premises;  for  we  might  know  that  James  was  a  Jew  and  that 
John  was  a  Jew,  and  so  on  through  the  twelve,  without 
knowing  or  without  thinking  that  these  twelve  were  all  the 
apostles. 

This  Perfect  Induction  is  relatively  rare;  for  it  is  only  in 
comparatively  few  cases  that  we  can  be  sure  that  the  indi- 
viduals named  constitute  the  whole  class  in  question. 

250 


PERFECT   INDUCTION.  251 

"  The  assertion  that  all  the  months  of  the  year  are  of  less 
length  than  thirty-two  days  ...  is  a  certain  conclusion 
because  the  calendar  is  a  human  institution,  so  that  we  can 
know  beyond  doubt  how  many  months  there  are.  .  .  .  But 
the  assertion  that  all  the  planets  move  in  one  direction  round 
the  sun,  from  West  to  East,  is  derived  from  Imperfect 
Induction;  for  it  is  possible  that  there  exist  planets  more 
distant  than  the  most  distant  known  planet  Neptune,  and  " 
of  "  such  a  planet  of  course  the  assertion  would  "  not  hold 
true.* 

If  a  being  who  was  purely  rational  found  that  a  Perfect 
Induction  was  impossible,  he  might  go  no  further.  But  wC- 
men  are  animals  as  well  as  rational,  and  have  an  Wlly  we 
animal's  tendency  to  react  to  every  impression,  accept  less. 
and  to  react  in  the  same  way  when  the  impressions  are 
similar.  Consequently  we  will  often  risk  a  conclusion  that 
the  premises  will  not  altogether  warrant,  and  when  all  the 
individuals  with  a  given  general  appearance  that  we  have 
examined  have  a  certain  particular  characteristic  we  almost 
always  take  it  for  granted  that  those  we  have  not  examined 
have  it  also.  "  Practically  in  inductive  argument  an 
opponent"  who  maintains  that  some  general  statement  is 
not  true  "  is  worsted  when  he  cannot  produce  an  instance 
to  the  contrary.  Suppose  he  admits  the  predicate  in  ques- 
tion to  be  true  of  this,  that,  and  the  other,  but  denies  that 
this,  that,  and  the  other  constitute  the  whole  class  in  ques- 
tion, he  is  defeated  in  common  judgment  if  he  cannot 
instance  a  member  of  the  class  about  which  the  predicate 
does  not  hold.  Hence  this  mode  of  induction  becomes 
technically  known  as  Inductio  per  enumerationem  sirnplicem 
ubi  non  reperitur  inslantia  contradictoria.  When  this  phrase 
is  applied  to  a  generalization  of  fact,  Nature  or  Experience 
is  put  figuratively  in  the  position  of  a  Respondent  unable  to 
contradict  the  inquirer."  f 

Thus  we  see  how  the  inductive  process  by  which  we  make 
*  Jevons'  "Lessons",  p.  213.  j  Minto,  pp.  236-7. 


252  THE   METHOD   OF   EXHAUSTION. 

and  try  to  justify  a  universal  proposition  falls  short  of  its 

ideal.  We  set  out  to  exhaust  the  universe,  and 
practical!1011  st°P  wnen  we  have  exhausted  our  own  knowledge 

or  when  we  get  tired  of  going  any^  further,  but 
we  draw  our  conclusion  nevertheless.  The  only  justification 
we  can  give  for  such  a  proceeding  is  practical ;  that  on  the 
whole  we  get  along  better  if  we  jump  to  such  conclusions 
after  a  reasonable  amount  of  investigation  than  if  we  always 
suspend  our  judgment  and  refuse  to  act  until  our  data  are 
absolutely  complete. 

How  many  cases  constitute  a  '  reasonable  '  number  upon 
which  to  base  a  general  conclusion  depends  altogether  upon 

circumstances.  If  the  general  conclusion  in 
we^Iue^f  question  fits  in  with  what  we  know  about  other 

things  it  will  not  usually  require  so  much  evi- 
dence in  its  favor  as  it  would  if  it  did  not.  In  view  of  what 
everybody  knows  about  other  animals  it  requires  very  little 
evidence  to  prove  that  all  sheep  are  mortal.  How  many 
cases  make  a  reasonable  number  depends  too  upon  how  likely 
it  is  that  we  should  know  of  an  exception  to  the  general  rule 
if  one  existed.  That  every  man  in  the  civilized  world  is  less 
than  twenty  feet  tall  we  have  a  right  to  say  at  once,  because 
we  know  that  if  taller  men  than  that  existed  anywhere  within 
the  bounds  of  civilization  we  should  be  sure  to  have  heard 
of  them.  A  third  consideration  which  helps  to  determine 
how  many  cases  we  should  investigate  before  venturing  upon 
a  general  statement  is  the  practical  importance  of  the  ques- 
tion at  issue.  If  the  eternal  salvation  of  every  human  being 
depended  upon  the  truth  of  our  statement  the  number  of 
cases  investigated  would  have  to  be  very  great  indeed  before 
any  one  of  us  would  think  it  reasonable  to  draw  the  general 
conclusion.  Anything  short  of  an  absolute  exhaustion  of 
the  group  in  question  fails  to  give  absolute  certainty,  and 
the  completeness  of  the  exhaustion  which  we  feel  compelled 
to  make  will  always  depend  upon  the  amount  of  certainty 
that  we  require. 


HOW  PROBLEMS  AND  RELATIONS  ARE  INTERWOVEN.    253 

Though  the  circumstances  which  help  to  determine  how 
much  evidence  for  a  general  conclusion  is  reasonable  are 
related  to  the  case  in  question,  they  all  lie  outside  of  it. 
That  is  to  say,  the  question  of  how  much  evidence  is  reason- 
able does  not  depend  so  much  upon  the  nature  of  the 
problem  in  itself  as  upon  its  relation  to  what  we  know  about 
other  things — e.g. ,  the  constitution  of  society  that  makes 
it  likely  that  we  should  hear  of  a  man  twenty  feet  tall  if  he 
existed,  the  supposed  divine  law  that  would  lead  to  our 
damnation  for  a  false  guess,  etc. 

The  one  thing  in  this  connection  which  the  student  of 
logic  should  not  overlook  is  this:  As  civilization  advances, 
the  need  for  accuracy  and  certainty  of  thought  and  action 
constantly  increases.  Our  environment  in  this  respect  is 
changing  very  rapidly,  while  our  natures  change  very  slowly. 
The  consequence  is  that  the  average  man  is  apt  to  be  too 
impatient  of  suspense  and  to  jump  to  his  conclusions  too 
rapidly  for  his  own  good.  And  if  the  individual  happens  to 
be  concerned  with  science,  in  the  very  front  of  the  forward 
movement,  where  the  need  for  accuracy  and  the  means  of 
attaining,  it  are  growing  most  rapidly,  then  intellectual 
patience  becomes  a  virtue  of  which  he  can  hardly  have  too 
much.  An  incautious  or  inaccurate  farmer  may  get  along 
after  a  fashion  even  in  this  day;  but  an  inaccurate  scientist 
is  almost  certainly  bound  to  be  an  utter  failure. 

Perfect  Induction  and  the  Inductio  per  Enumerationem 
Simplicem  may  be  regarded  as  the  inductive  processes  corre- 
sponding   to    the   first   figure   of   the  syllogism. 
They  are  not  concerned  pre-eminently  with  any   problems 
particular    kind    of   relations;    they   involve   no   tionsare 
refined  analysis;  and  their  only  positive  charac- 
teristic is  the  generality  of  their  conclusions. 

On  page  225  we  saw  how  the  principle  of  exhaustion  is 
used  to  ascertain  relations  of  identity  and  causation  as  well  as 
to  prove  propositions  that  are  merely  general ;  and  how  the 
principle  therefore  furnishes  an  inductive  process  correspond- 


254  THE  METHOD   OF   EXHAUSTION. 

ing  to  each  figure  of  the  syllogism.  In  the  case  of  the 
general  proposition  the  method  of  exhaustion  is  one  of  addi- 
tion,— such  and  such  a  thing  is  true  of  this  and  that  and  the 
other,  therefore  of  all.  In  the  case  of  identity  and  causation 
the  method  of  exhaustion  is  one  of  subtraction  or  elimina- 
tion,— the  thing  or  the  cause  in  question  cannot  be  this  or 
that,  therefore  it  must  be  the  other.  This  method  of  elimi- 
nation would  not  be  possible  unless  we  were  sure  enough  of 
the  uniformity  of  nature  to  assume  that  a  thing  identical 
with  the  one  in  question  or  that  a  cause  for  the  given  event 
must  surely  exist  somewhere. 

It  is  noteworthy  that  in  practice  questions  concerning 
general  truths,  concerning  identity  and  concerning  causation 
are  interwoven  in  many  ways.  When  we  have  proved  either 
by  a  '  perfect  induction  '  or  by  the  Inductio  per  Enumera- 
tionem  Simplicem  that  everything  with  the  characteristic 
A  has  also  the  characteristic  B  we  can  hardly  avoid  suspect- 
ing that  between  A  and  B  there  is  some  rather  direct  relation 
of  causation.  Conversely  we  can  prove  that  everything  with 
the  characteristic  A  has  also  the  characteristic  B  without  the 
Perfect  Induction  or  Inductio  per  Enumerationem  Simplicem 
if  we  have  any  means  of  proving  that  A  inevitably  causes  B. 
So  with  Identity.  A  person  can  be  sure  that  the  book  he 
finds  in  a  certain  library  to-day  is  the  one  he  left  there 
yesterday  if  he  can  prove  that  it  is  the  only  book  like  his 
that  is  now  in  the  library,  and  that  no  books  have  gone  out 
and  come  in  since  his  was  left.  But  how  can  one  be 
sure  that  a  book  has  not  gone  out  of  the  library  and  another 
come  in  to  take  its  place  ?  Is  it  not  only  because  he  knows 
that  books  cannot  pass  through  solid  walls  or  throw  them- 
selves spontaneously  through  windows  and  doors,  and 
because  he  knows  also  that  if  anybody  had  carried  one  book 
in  and  another  out  the  librarian  would  have  seen  him  or  the 
lock  on  the  door  would  have  been  broken,  or  some  other 
perceptible  change  would  have  been  caused,  when  it  was 
not  ? 


HOW  PROBLEMS  AND  RELATIONS  ARE   INTERWOVEN.    255 

In  this  way  knowledge  of  causal  relations  helps  us  to 
prove  identity  just  as  it  may  help  us  to  prove  the  truth  of  a 
universal  proposition.  Such  a  case  as  this  is  not  excep- 
tional. We  prove  that  the  comet  now  visible  is  the  one  that 
appeared  ten  years  ago  because  calculations  made  at  that 
time  showed  that  at  precisely  this  time  it  must  appear  at  the 
very  spot  where  a  comet  is  now  seen;  and  since  there  cannot 
be  two  comets  in  the  same  place  the  one  we  see  now  must 
be  the  one  we  saw  then.  So  too  when  a  '  medium  '  tries 
to  prove  to  you  that  the  spirit  with  which  she  now  claims 
to  be  in  communication  really  is  the  spirit  of  your  departed 
friend  she  tries  to  show  that  the  spirit  does  and  knows  what 
nobody  but  that  friend  would  or  could  do  or  know;  and 
thus  she  leaves  this  problem  on  your  hands:  If  my  friend 
did  not  speak  through  the  medium,  how  in  the  world  am  I 
to  account  for  all  the  things  the  medium  or  the  spirit  that 
spoke  through  her  did  ?  In  the  same  way  once  more,  when 
a  prosecuting  attorney  tries  to  prove  that  the  prisoner  before 
the  court  was  the  person  who  broke  into  the  bank  he 
attempts  to  show  that  there  is  some  effect  which  could  not 
possibly  have  been  produced  if  the  burglary  had  been  com- 
mitted by  anybody  else.  Thus  a  question  of  identity,  like 
the  question  of  the  truth  of  some  general  statement,  can  be 
resolved  into  a  question  of  causation. 

So,  vice  versa,  when  we  are  investigating  a  question  of 
causation  we  always  take  for  granted  various  relations  of 
identity  and  various  relations  of  kind  such  as  are  expressed 
in  general  propositions.  When  we  conclude  that  a  certain 
man  must  have  been  poisoned  by  arsenic  because  nothing 
else  would  have  caused  the  same  symptoms  we  assume  the 
existence  of  the  man  and  of  the  arsenic  as  real  things  retain- 
ing their  identity  from  the  time  of  the  supposed  poisoning  to 
the  time  that  the  symptoms  appeared.  We  also  assume  that 
every  bit  of  arsenic  has  the  same  nature  as  every  other  bit 
and  acts  in  the  same  way  under  the  same  conditions,  and 
that  men  also  are  similar  to  each  other,  so  that  at  least  some 


256  THE  METHOD   OF  EXHAUSTION. 

of  the  symptoms  produced  by  the  arsenic  are  substantially 
alike  in  them  all. 

In  courts  of  law  individuals  as  such  are  everything,  and 
general  laws  or  rules  of  action  are  only  means  for  adjusting 
their  conflicting  claims.  Consequently  problems  of  identity 
in  the  courts  are  all-important,  and  all  sorts  of  devices  are 
resorted  to  for  answering  such  questions  as  whether  or  not 
this  particular  man  is  the  one  that  owned  this  particular 
horse  or  signed  this  particular  bit  of  paper.  But  with  science 
it  is  different;  for  scientists  have  very  much  more  to  say  about 
the  conditions  under  which  certain  effects  are  produced  than 
about  the  identity  of  the  agents.  Since  the  chemist  assumes 
all  atoms  of  hydrogen  to  be  alike  he  neither  knows  nor  cares 
whether  the  one  involved  in  a  given  reaction  is  Atom  No.  49 
or  Atom  No.  63.  His  identification  stops  when  he  finds  out 
that  the  atom  in  question  is  some  one  or  other  of  the  many 
billions  of  similar  atoms  that  we  call  hydrogen,  and  that  it 
has  recently  been  put  through  such  and  such  a  process. 
For  that  particular  atom  as  such  he  cares  not  a  snap  of  his 
finger.  Its  only  value  for  him  is  to  show  what  any  atom  of 
the  sort  will  do  under  a  given  set  of  conditions.  This  dis- 
tinction, however,  is  not  absolute.  The  jury  in  a  trial  for 
murder  has  to  determine  whether  the  injury  inflicted  by  the 
prisoner  upon  the  deceased  really  was  the  cause  of  his  death, 
and  such  sciences  as  geology  and  history  are  concerned  very 
largely  with  the  question  of  what  individual  person  or  thing 
it  was  that  produced  this  or  that  given  effect.  After  all,  the 
question  of  identity  and  the  question  of  circumstance  are 
inextricably  interwoven;  for  thing  and  circumstance  are 
only  different  aspects  of  the  same  concrete  fact  and  neither 
could  act  or  even  exist  without  the  other. 


CHAPTER    XXV. 

INDUCTION  BY   SIMPLE  ENUMERATION  AND  THE  SEARCH 
FOR  CAUSES. 

THE  Inductio  per  Enumerationem  Simplicem  is  regarded 
by  scientists  nowadays  as  a  primitive  and  unsatisfactory 
kind  of  inference  that  should  be  replaced  or  sup- 
plemented wherever  possible  by  an  inference 
based  upon  the  knowledge  of  causes.  The  essen- 
tial  difference  between  the  two  methods  is  that 
the  one  based  upon  a  knowledge  of  causes  involves  analysis 
and  the  other  does  not.  Inductio  per  Enumerationem  Sim- 
plicem takes  each  of  the  observed  relations  in  the  mass  just 
as  it  stands,  notices  how  often  they  coincide,  and  then  makes 
a  guess  about  the  future.  Causal  analysis  is  not  content  to 
take  the  observed  uniformities  so  roughly ;  but  splits  them 
up,  in  order  to  find  the  simpler  and  more  general  uniformi- 
ties which  are  involved.  And  then  when  this  is  done  it  may 
try  to  determine  the  conditions  under  which  they  will  work 
together  in  the  same  way  again.  An  inference  based  upon 
the  knowledge  of  causes  is  therefore  based  upon  a  definite 
knowledge  of  all  the  details  rather  than*  upon  a  confused  im- 
pression of  a  whole. 

A  farmer  may  happen  to  notice  that  red  clover  grows 
better  near  the  homes  of  old  maids  than  elsewhere  in  the 
neighborhood.  Reasoning  per  enumcrationcm  simplicem  he 
might  conclude  that  there  is  always  something  about  an  old 
maid  that  helps  the  growth  of  clover.  But  he  would  have  no 

257 


SIMPLE    ENUMERATION   AND   CAUSAL   ANALYSIS. 

means  of  knowing  how  much  faith  should  be  attached  to  this 
-conclusion.  He  could  not  say  how  likely  it  was  that  the  next 
case  he  noticed  would  conform  to  the  rule.  But  suppose  he 
should  happen  to  think  that  old  maids  often  keep  cats,  that 
cats  kill  mice,  that  mice  destroy  bumblebees,  and  that  with- 
out bumblebees  to  carry  the  pollen  from  one  plant  to  another 
red  clover  cannot  develop  its  seed.  Then  he  would  have 
broken  up  the  first  uniformity — between  the  old  maids  and 
the  clover — into  a  series  of  others,  most  of  which,  at  least, 
are  much  more  familiar  and  therefore  much  more  thoroughly 
tested;  he  would  know  almost  exactly  how  much  reliance  could 
be  placed  upon  each  of  them  ;  and  putting  them  all  together  he 
could  say  without  any  hesitation  whatever  whether  it  is  always 
true  that  old  maids  help  the  clover-meadows.  In  this  way,  a 
knowledge  of  causes  gives  much  greater  certainty  than  the 
bare,  unanalytic  Inductio  per  Enumerationem  Simplicem. 

In  this  example,  as  in  almost  any  other  that  might  be 
given,  the  analysis  into  causes  or  simpler  uniformities  is  very 
incomplete.  Each  of  the  causal  relations  given  might  be 
itself  reduced  to  others  still  simpler.  That  old  maids  keep 
cats  ;  that  cats  kill  and  eat  mice  ;  that  mice  destroy  the  nests 
and  young  of  bumblebees;  and  that  red  clover  needs  these  bees 
to  fertilize  it  :  all  these  may  be  themselves  mere  Inductiones 
per  Enumerationem  Simplicem,  about  which  we  may  feel 
sceptical ;  and  we  may  wish  to  test  any  or  all  of  them  by 
finding  the  still  simpler  uniformities  that  would  account  for 
them  if  they  really  existed.  If  cats  do  always  eat  mice,  the 
mice  are  probably  good  for  them;  if  mice  are  good  for  cats 
to  eat,  it  must  be  because  they  can  be  digested  and  pass  into 
the  system;  if  digested  food  passes  into  the  system  of  a  cat 
or  any  other  animal,  it  must  be  because  it  can  get  through 
the  membranes  lining  the  alimentary  canal  ;  if  food  can  get 
through  these  membranes,  it  must  be  because  certain  fluids  will 
pass  through  moist  membranes  anywhere.  In  this  way  one 
uniformity  after  another  can  be  reduced  to  others  still  more 
general,  until  we  can  carry  the  process  no  further  and  we 


ANALYSIS   AND   CLEAR   THINKING.  259 

have  to  content  ourselves  at  last  with  certain  simple  laws  of 
chemistry  and  physics. 

When  any  event  is  shown  to  have  taken  place  in  accordance 
with  uniform  laws,  or  when  some  uniformity  is  reduced  to 
others  more  simple  and  more  general  it  is  said  to  be  '  ex- 
plained '.  The  simplest  and  most  general  laws  of  all  must 
be  accepted  without  explanation  on  the  strength  of  an  In- 
ductio  per  Enumerationem  Simplicem.  The  most  that  we 
can  say  for  the  existence  of  any  of  them  is  that  they  seem  to 
be  involved  by  a  vast  number  of  experiences  and  to  be  con- 
tradicted by  none.* 

When  we  find  the  causes  back  of  any  observed  uniformity, 
the  things  with  which  we  started  become  more  fully  known 
as  well  as  the  relations  between  them,  and  the 

knowledge  of  both  things  and  relations  in  becorn-   and  clear 
r  11      i  i  T     ^  i      thinking. 

ing  fuller  becomes  also   clearer.      In  the  example 

given  '  red  clover  '  took  a  definite  character  as  a  plant  depend- 
ent for  its  propagation  upon  cross-fertilization  by  an  insect 
able  to  reach  its  nectar,  and  if  we  had  asked  why  the  pollen 
must  be  carried,  why  the  bumblebee  is  better  able  to  get  at 
the  nectar  than  other  insects,  and  so  on,  we  should  have  gained 
still  clearer  and  fuller  ideas  about  the  clover.  As  the  rela- 
tions with  which  we  begin  are  not  fully  analyzed  and  ex- 
plained until  they  are  reduced  to  ultimate  laws,  so  the  things 
with  which  we  start  are  not  completely  understood  until  each 
of  them  is  analyzed  at  last  into  a  definite  group  of  various 
kinds  of  atoms. 

The  clearness  and  definiteness  of  thought  which  causal 
analysis  gives  is  as  valuable  in  itself  as  the  greater  certainty  of 
inference  that  goes  along  with  it.  General  appearances  ob- 

*  The  sociologist,  for  example,  cannot  get  along  without  assuming 
certain  laws  of  mind  ;  the  psychologist  tries  to  account  for  mental  laws 
by  reference  to  nerve-physiology  ;  the  physiologist  tries  to  reduce  his 
data  to  laws  of  chemistry  and  physics  ;  the  chemist  tries  to  explain  his 
data  by  molecular  physics;  and  the  physicist  tries  to  state  all  his  facts 
in  the  formula;  of  mathematics. 


260   SIMPLE   ENUMERATION   AND   CAUSAL   ANALYSIS. 

scurely  apprehended  are  often  sufficient  to  call  forth  a  fairly 
definite  and  appropriate  reaction  on  our  part.  The  lines  on 
a  companion's  face  may  be  quite  indescribable  by  us  and  yet 
suggest  the  words  '  He  is  angry  '.  In  the  same  way  a  number 
of  very  indescribable  impressions  may  suggest  the  word'  Iron  ' 
or  'Bewitched'  or  'Tyrannizing'.  These  vague  impres- 
sions are  valuable  because  the  words  and  other  reactions  to 
which  they  lead  are  generally  fairly  appropriate  and  useful. 
And  yet  real  things  and  relations  are  never  vague,  and  vague 
impressions  can  never  represent  them.  They  do  not  pre- 
cisely misrepresent  them,  for  vague  ideas  neither  represent 
nor  misrepresent,  since  they  cannot  be  measured  ngainst  the 
facts  at  all.  How  can  we  ever  prove  that  Mother  Hubbard 
does  not '  hoodoo  '  her  dog  or  '  project  '  her  thoughts  in  such 
a  way  as  to  'impress  '  the  brain  of  the  Czar,  until  we  know 
precisely  what  it  means  to  be  '  hoodooed  '  or  what  a  '  pro- 
jected '  thought  is  supposed  to  do  to  the  brain  that  it  '  im- 
presses'?  Hence  if  one's  expectations  are  only  vague  enough 
there  is  no  such  thing  as  definite  fulfilment  or  definite  dis- 
appointment. Definite  conceptions,  on  the  other  hand,  can 
represent  realities ;  and  therefore  there  is  some  chance  of 
having  one  that  does.  If  it  does  not,  its  very  defmiteness 
makes  it  possible  to  prove  that  it  does  not.  If  it  does,  we  can 
count  upon  it  always.  Thus  a  second  reason  for  seeking  to 
reduce  observed  uniformities  to  their  causes  is  the  clearness 
of  conception  which  it  gives. 


CHAPTER   XXVI. 

THE   METHODS   OF   DIFFERENCE  AND   AGREEMENT. 

IN  the  preceding  chapters  we  have  discussed  the  general 
principles  involved  in  inductive  reasoning.  We  must  now 

see  how  the  principles  are  applied  to  various  kinds 

,  Different 

of  concrete  problems.     We  have  seen  already  that  ways  of 

11  i       j-    -j    j  LI      •    ^  exhausting: 

these  problems  may  be  divided  roughly  into  two  thenni- 

classes :    the    discovery  or   verifying  of  general 
laws,    and   the    ascertaining   of  concrete    individual    facts. 
Questions  of  concrete  fact  will  not  be  discussed  until  after 
we  come  to  Chapter  XXXIII.     At  present  we  shall  consider 
only  questions  of  general  law. 

The  principles  involved  in  these  questions  are  always  the 
same,  yet  there  are  differences  in  the  data  to  which  they  are 
applied  which  involve  corresponding  differences  in  the  ap- 
plications ;  and  if  our  knowledge  of  the  principles  is  to  have 
any  richness,  we  ought  to  know  something  about  these  differ- 
ent ways  in  which  they  are  applied.  The  most  striking  appli- 
cations are  to  be  found  in  scientific  investigations.  Many  of 
these  are  described  in  Herschel's  "  Discourse  on  the  Study 
of  Natural  Philosophy"  (1832)  and  in  Whewell's  two  large 
volumes  on  the  "  History  of  the  Inductive  Sciences  "  (1837) 
and  his  "Philosophy  of  the  Inductive  Sciences"  (1840), 
from  which  subsequent  writers  have  drawn  much  of  their 
material.  With  the  facts  and  theories  of  these  writers  before 
him  John  Stuart  Mill  set  out  in  his  "Logic"  (published  in 
1843)  to  'generalize  the  modes  of  investigating  truth  and 

261 


262   THE   METHODS   OF   DIFFERENCE   AND   AGREEMENT. 

estimating  evidence,  by  which  so  many  important  and  recon- 
dite laws  of  nature  have,  in  the  various  sciences,  been  ag- 
gregated to  the  stock  of  human  knowledge',  and  Mill's 
chapter  on  "The  Four  Methods  of  Experimental  Inquiry" 
contains  the  classical  account  of  the  various  ways  in  which 
the  principle  is  applied  for  the  discovery  of  causal  relations.* 
These  different  ways  of  applying  the  principle  are  called  by 
Mill  the  Method  of  Agreement,  the  Method  of  Difference 
(including  the  Joint  Method  of  Agreement  and  Difference,  or 
Indirect  Method  of  Difference),  the  Method  of  Residues,  and 
the  Method  of  Concomitant  Variations.  We  shall  give  an 
account  of  each  of  them,  beginning  with  the  Method  of  Dif- 
ference. 

If  a  baby  strikes  or  pushes  a  hanging  ball  and  the  ball 
moves,  and  if  the  experience  happens  to  be  repeated  several 

times,  the  babv  gets  in  the  way  after  a  while  of  ex- 
The  Method 

of  Differ-  peeling  that  each  new  stroke  or  push  will  be  fol- 
lowed by  a  new  movement  of  the  ball,  and  years 
afterwards  it  learns  to  say  that  the  stroke  of  the  hand  caused 
the  movement  of  the  ball.  If  a  man  were  to  try  the  same 
experiment  as  the  child  he  would  reach  the  same  conclusion, 
but,  unlike  the  child,  he  might  try  to  explain  why  the  con- 
clusion was  reasonable.  If  he  did,  his  reasoning  would  be 
something  like  this :  '  Before  I  touched  the  ball  it  was  mo- 
tionless. I  struck  it  a  great  many  times.  Every  time  I 
struck  it  it  moved.  When  I  left  it  alone  it  gradually  stopped 
moving.  If  my  blows  did  not  move  it,  what  did?  I  was 

*  It  is  hardly  necessary  to  say  that  inductive  inquiry  existed  long 
before  the  theories  of  these  writers,  and  even  a  very  clear  theoretical 
conception  of  the  principles  on  which  it  is  founded.  Minto's  "Logic" 
(pp.  243-272)  gives  a  good  account  of  the  whole  matter,  including  the 
views  and  influence  of  Francis  Bacon  and  of  Roger  Bacon  (1214-1292), 
whom  Minto  calls  his  greater  namesake.  Minto,  however,  does  not  men- 
tion Hume  and  his  remarkably  clear  statement  of  the  canons  for  the 
methods  of  Agreement,  Difference,  and  Concomitant  Variations  (See 
the  '  Rules  by  which  to  judge  of  causes  and  effects  '  in  the  "  Treatise  of 
Human  Nature"). 


THE   METHOD   OF   DIFFERENCE.  263 

alone  in  the  room  ;  the  house  was  quiet ;  there  were  no  sud- 
den draughts  of  air.  It  may  be  that  a  ball  might  be  moved 
before  my  eyes  by  some  cause  that  I  could  not  see  and  do 
not  know  about ;  but  if  there  was  any  such  cause,  why  did  it 
always  wait  to  move  the  ball  until  I  struck  it  ? ' 

The  force  of  this  argument  lies  in  the  question  '  If  I  did 
not,  what  did  ?  '  The  man  assumes  that  the  event  must  have 
been  caused,  and  the  harder  he  looks  without  finding  any- 
thing that  might  have  caused  it  except  his  own  activity  the 
surer  he  feels  that  that  was  the  real  cause ;  and  if  he  knew 
for  certain  that  his  blow  was  the  only  change  introduced 
into  the  situation  before  the  ball  began  to  move — the  only 
point  of  difference  except  the  movement  itself  between  the 
situation  in  which  the  ball  did  not  move  and  that  in  which  it 
did — then  he  could  be  absolutely  certain  that  it  was  his  blow 
that  caused  the  movement  of  the  ball.  It  is  clear  enough 
that  this  reasoning  is  based  on  our  principle  of  exclusion  (one 
of  the  forms  taken  by  the  wider  principle  of  exhaustion,  see 
p.  225)  ;  and  the  italicized  words  explain  why  Mill  calls 
this  special  application  of  the  principle  the  Method  of  Dif- 
ference. 

It  makes  no  difference  in  the  method  whether  it  is  used  to 
explain  an  actual  change  in  one  situation  or  the  difference 
between  two.  If  there  are  two  precisely  similar  balls  sus- 
pended in  precisely  similar  manners,  except  that  one  is 
exposed  to  a  steady  wind  and  moving  while  the  other  is 
sheltered  and  stationary,  we  can  conclude  that  the  wind  is 
the  only  possible  cause  of  the  movement,  since  it  is  the  only 
circumstance  (except  the  movement  itself)  present  in  one 
case  and  not  in  the  other  and  we  cannot  suppose  that  a  cir- 
cumstance present  in  both  cases  would  move  one  ball  which 
happens  to  be  here  and  not  move  another  precisely  like  it 
which  happens  to  be  there. 

The  principle  of  exclusion  as  used  in  this  method  of  dif- 
ference can  be  stated  in  the  following  abstract  canon  of 
Mill's:  "  If an  instance  in  which  the  phenomenon  under  in- 


264   THE   METHODS   OF   DIFFERENCE   AND   AGREEMENT. 

vestigation  occurs,  and  an  instance  in  which  it  does  not  occur, 
have  every  \olher~^  circumstance  in  common  save  one,  that  one 
occurring  only  in  the  former  ;  ike  circumstance  in  which  alone 
the  two  instances  differ,  is  the  effect,  or  the  cause,  or  an  indis- 
pensable part  of  the  cause,  of  the  phenomenon."  To  put  the 
same  thing  more  symbolically:  If  there  is  a  case  in  which 
all  the  antecedents  can  be  represented  by  the  letters  A,  B,  C, 
and  D  and  all  the  consequents  by  the  letters  W,  X,  Y,  and 
Z,  and  another  case  in  which  all  the  antecedents  can  be 
represented  by  the  letters  A,  B,  and  C,  and  all  the  conse- 
quents by  W,  X,  and  Y,  then  the  antecedent  D  is  the  cause 
or  part  of  the  cause  of  the  consequent  Z. 

A  girl  dressed  in  a  blue  gown  and  carrying  some  books 
walks  quietly  across  a  room  and  as  she  passes  over  a  certain 

place  a  squeaky  noise  is  heard.      Soon  after,  a 
The  Method      ,  l,       .     „       ...... 

of  Agree-  boy  dressed  wholly  differently,  talking,  and  car- 
rying nothing  at  all,  walks  over  the  same  place, 
and  as  he  does  so  the  noise  is  heard  again.  Now  if  we 
assume  that  the  noise  has  the  same  cause  in  both  cases  and  if 
we  can  be  sure  that  walking  over  the  same  spot  was  the  only 
circumstance  except  the  noise  that  was  the  same  in  both, 
i.e.,  the  only  one  in  which  the  two  instances  agreed,  then  we 
cannot  help  concluding  that  walking  over  that  spot  caused 
the  noise.  The  italicized  words  explain  why  this  inference 
is  drawn  by  the  Method  of  Agreement. 

This  method,  like  the  last,  depends  on  the  principle  of  ex- 
clusion; for  we  cannot  be  sure  that  the  circumstance  we  have 
picked  out  is  the  only  point  of  agreement  until  we  have  ex- 
amined every  other  circumstance  and  found  that  no  one  of 
them  is  the  same  in  both  cases. 

In  the  example  just  given  the  effect  was  produced  at  the 
time  of  the  observation,  so  that  the  things  involved  underwent 
a  change.  But  the  method  of  agreement  is  also  applicable  to 
cases  in  which  we  cannot  observe  the  origin  of  the  effect. 
Suppose,  for  example,  that  on  the  top  of  every  high  mountain 


DOES   EITHER   METHOD   REALLY   EXHAUST?        265 

which  we  climb  we  find  the  air  to  be  cooler  than  in  the  sur- 
rounding country,  no  matter  where  the  mountains  are,  what 
their  shape,  or  what  they  are  made  of.  As  soon  as  we  can  be 
sure  that  the  elevation  is  the  only  point  of  agreement  between 
them  all  (except  the  lower  temperature)  we  can  infer  that  the 
greater  elevation  has  something  to  do  with  the  lower  temper- 
ature. 

Mill's  canon  for  the  method  of  agreement  is  this:  "  Tf 
two  or  more  instances  of  the  phenomenon  under  investigation  have 
only  one  circumstance  in  common  [and  if  that  phenomenon  is 
always  produced  by  the  same  circumstance  ;  then]  the  circum- 
stance in  which  alone  all  the  instances  agree  is  the  cause  (or 
effecf)  of  the  given  phenomenon."  To  put  it  more  symboli- 
cally :  If  all  the  antecedents  in  one  case  can  be  represented 
by  the  letters  ABCD  and  all  the  consequents  by  WXYZ, 
and  in  another  case  all  the  antecedents  can  be  represented 
byEFGD  and  all  the  consequents  by  KLMZ,  and  if  Z  always 
has  the  same  cause,  then  D  is  the  cause  of  Z. 

The  methods  of  agreement  and  difference  both  depend 
upon  the  principle  of  exclusion,  and  in  both  methods  this 
principle  has  been  properly  applied  only  if  we  Doeseitter 
have  been  correct  in  assuming  that  no  point  of  ^arLyW- 
agreement  or  difference  (as  the  case  may  be)  es-  haust  ? 
caped  our  observation.  But  this  is  no  small  assumption.  How 
do  we  know  that  the  mountains  we  visit  do  not  happen  by  the 
merest  chance  to  lie  over  relatively  cool  places  in  the  centre  of 
the  earth,  or  to  be  packed  with  ice,  or  to  lie  in  places  where 
cool  currents  of  air  turn  downwards  towards  the  earth  ?  How 
do  we  know  that  when  the  girl  and  the  boy  both  passed  the 
same  spot  a  cat  in  the  cellar  did  not  happen  to  catch  a  mouse 
which  made  the  noise  as  it  was  caught  ?  How  do  we  know 
that  the  ball  the  child  struck  was  not  possessed  by  a  demon 
which  happened  to  move  it  at  that  instant,  and  that  the  one 
swinging  in  the  wind  was  not  similarly  possessed  ?  In  short, 
it  is  only  an  infinitesimal  part  of  nature  that  we  can  pretend 
to  have  observed,  and  how  can  we  possibly  prove  that  the 


266   THE   METHODS   OF   DIFFERENCE   AND   AGREEMENT. 

only  point  of  agreement  or  the  only  point  of  difference  we 
happen  to  have  noticed  is  the  only  one  there  is  ? 

We  can  not ;  and  for  that  reason  our  inductive  argument 
will  always  be  at  least  theoretically  inconclusive.  But  all 
reasoning,  even  deductive,  is  for  the  sake  of  practice ;  and 
from  the  practical  standpoint  the  force  of  this  objection  can 
be  considerably  weakened.  As  mere  theorists  the  thought  of 
the  almost  infinite  search  that  must  be  made  before  we  can  say 
we  have  found  the  only  point  of  agreement  or  the  only  point 
of  difference  between  two  situations  appals  us.  As  practical 
beings  it  does  not  ;  for  when  we  begin  to  reason  about  the 
connections  in  Nature  we  are  not  in  the  position  of  strangers 
dropped  from  another  universe.  We  are  in  the  midst  of 
affairs.  We  have  learned  in  a  practical  way  that  a  vast  num- 
ber of  agreements  and  differences  between  situations  can  be 
thrown  out  immediately  as  immaterial  ;  and  we  dismiss  them 
so  unhesitatingly  that  \ve  are  inclined  to  laugh  at  the  theorist 
instead  of  answering  him  when  he  asks  how  we  know  that  the 
ball  did  not  swing  because  a  Chinaman  laughed  on  the  other 
side  of  the  globe,  or  that  the  mountains  we  saw  were  not  cool 
because  people  lived  in  the  valleys.  Thus  the  practical  man 
approaches  his  inductive  problem  with  vastly  more  data  than 
he  states  ;  he  does  not  hesitate  to  distinguish  between  kinds 
of  agreement  and  difference  that  may  be  material  and  those 
that  are  certainly  immaterial  ;  and  thus  most  of  the  elimina- 
tion is  already  performed. 

Not  only  have  we  this  practical  belief  that  the  possible 
causes  are  after  all  not  so  very  numerous,  but  we  have  it  in  our 
power  to  diminish  the  chance  that  any  of  them  have  been  over- 
looked by  observing  as  many  and  as  different  cases  as  possible. 

The  more  mountains  we  examine  and  the  more  differenc 
there  seems  to  be  between  them  in  every  respect  except 
height  and  coolness,  the  greater  is  the  chance  that  there  is  no 
oilier  point  of  resemblance  common  to  them  all.  The  more 
often  we  notice  that  light  things  begin  to  move  when  the 
wind  begins  to  blow,  the  less  chance  there  is  that,  in  every 


ADVANTAGES   OF   EACH.  267 

case  we  noticed,  some  entirely  different  event  (which  we  did 
not  notice  but  which  might  have  caused  the  movement)  took 
place  at  the  very  instant  the  wind  rose.  Mere  coincidences — 
whether  in  space  or  in  time — may  be  expected  occasionally, 
but  occasionally  only. 

Whether  we  shall  use  the  Method  of  Difference  or  the 
Method  of  Agreement  in  any  particular  case  often  depends 
upon  what  data  we  have  to  work  with ;  and  Advantages 
therefore  we  cannot  always  choose  between  them.  of  each< 
It  is  worth  while  nevertheless  to  discuss  some  of  their  relative 
advantages  and  disadvantages. 

The  methods  of  Difference  and  Agreement  are  both  subject 
to  the  defect  already  pointed  out  that  we  may  fail  to  observe 
or  consider  some  essential  circumstance,  and  may  thus  mis- 
take some  merely  accidental  concomitant  for  the  true  cause. 
With  the  method  of  Difference  the  circumstance  overlooked 
would  be  a  point  of  difference  between  the  objects  com- 
pared ;  with  the  method  of  Agreement  it  would  be  a  point 
of  agreement. 

A  much  more  certain  and  important  difference  in  the 
practical  application  of  the  two  methods  grows  out  of  the 

fact  that  much  the  same  result  can  often  be  pro- 

r  .  ,T  Plurality  of 

duced  by  any   one  of  several   causes.      You  can    possible 
....  .  ,.,-,.  causes, 

kill  a  man  in  a  great  many  different  ways  ;    you 

can  poison  him  with  any  one  of  a  great  many  different  drugs. 
Rain  is  not  the  only  thing  that  can  wet  a  lawn  ;  and  sunshine 
is  not  the  only  thing  that  can  dry  it.  This  is  called  the  princi- 
ple of  the  Plurality  of  Possible  Causes  or  the  Vicariousness  of 
Causes.  Let  us  see  how  it  affects  each  of  our  methods. 

If  we  find  the  antecedents  ABC  accompanied  by  the  con- 
sequents XYZ,  and  the  antecedents  AB  accompanied  by  the 
consequents  XY,  and  if  we  know  that  these  are  all  the  essen- 
tial facts,  we  can  conclude  that,  under  the  circumstances 
AB,  C  is  the  cause  or  a  necessary  part  of  the  cause  of  Z. 
This  is  the  method  of  difference,  and  it  is  not  affected  by  the 
plurality  of  possible  causes. 


268   THE  METHODS   OF   DIFFERENCE   AND   AGREEMENT. 

But  suppose  that  in  one  case  we  have  the  antecedents  ABC 
and  the  consequents  XYZ,  and  in  another  the  antecedents 
EFC  and  the  consequents  VWZ,  and  that  these  are  all  the 
essential  circumstances.  If  Z  has  the  same  cause  in  both 
cases,  we  know  that  it  cannot  be  anything  but  C  ;  but  it  need 
not  have  the  same  cause  in  both  cases.  How  do  we  know, 
then,  that  it  is  not  caused  by  A  in  one  case  and  by  E  in  the 
other?  If  I  have  coffee,  toast,  and  eggs  for  breakfast  one 
day,  and  water,  hot  biscuit,  and  eggs  the  next,  and  if  I  have 
indigestion  on  both  days  and  know  or  assume  that  in  each 
case  it  was  caused  by  something  which  I  had  for  breakfast, 
it  may  have  been  caused  by  the  eggs  on  both  occasions ; 
and  in  the  absence  of  any  further  information  that  is  the 
most  natural  inference.  And  yet  it  is  possible  that  the 
trouble  was  due  to  the  coffee  on  the  first  day  and  to  the  hot 
biscuit  on  the  second,  while  the  eggs  were  all  the  time  per- 
fectly harmless. 

This  plurality  of  possible  causes  constitutes  what  Mill  calls 
"the  characteristic  imperfection"  of  the  Method  of  Agree- 
ment,— an  imperfection  which  makes  it  distinctly  inferior  to 
the  Method  of  Difference. 

,Where  answers  suggested  by  the  method  of  agreement 
cannot  be  tested  by  some  form  of  the  method  of  difference, 
the  uncertainty  arising  from  the  plurality  of  possible  causes 
can  be  indefinitely  diminished  by  the  multiplication  of  vari- 
ations. If  we  cannot  try  the  eggs  alone,  it  may  be  that  we 
can  try  them  with  different  accompaniments  on  a  great  many 
different  days,  until  we  are  driven  to  the  conclusion  that  if 
they  do  not  cause  the  trouble,  they  are  about  the  only  things 
one  can  eat  that  do  not.  But  farther  than  this  we  cannot 
go  by  the  Method  of  Agreement  ;  and  it  is  not  often  we  can 
go  so  far. 

This  difficulty  growing  out  of  the  plurality  of  possible 
causes  I  have  spoken  of  as  practical.  It  is  due  partly  to  the 
practical  impossibility  of  ascertaining  all  the  antecedents  and 
all  the  consequents  in  any  set  of  cases,  partly  to  the  practical 


PLURALITY   OF   POSSIBLE   CAUSES.  269 

impossibility  of  distinguishing  with  absolute  accuracy  or  cer- 
tainty between  relevant  and  irrelevant  circumstances,  and 
partly  to  our  careless  way  of  ignoring  the  distinction  between 
different  conditions  so  long  as  they  are  called  by  the  same 
name.  So  long  as  we  know  merely  that  '  we  have  indiges- 
tion after  breakfast '  in  all  the  cases  mentioned,  we  cannot 
toll  whether  it  was  caused  by  the  same  thing  every  time  or 
by  different  things  ;  but  if  we  took  the  trouble  to  find  out 
each  day  how  soon  after  the  meal  the  attack  arose,  precisely 
how  severe  it  was,  how  long  it  lasted,  and  every  other  ob- 
servable detail,  we  should  soon  be  able  to  say  whether  the 
trouble  really  was  the  same  in  all  the  cases,  as  our  first,  rough 
statement  implied,  or  in  fact  quite  different.  If  it  was  pre- 
cisely the  same  in  every  relevant  respect,  we  could  be  quite 
sure  that  in  each  case  the  attack  was  caused  by  the  same 
thing — namely,  the  eggs  ;  but  if  we  found  constant  variations 
in  the  symptoms,  and  if  we  could  be  sure  (as  we  cannot) 
that  variations  in  the  things  eaten  for  breakfast,  as  distin- 
guished from  previous  conditions  or  the  manner  of  eating, 
were  the  only  possible  cause  of  these  variations,  and  that  the 
eggs  eaten  were  all  precisely  alike  in  every  essential  respect, 
then  we  could  be  quite  certain  that  the  eggs  were  not  the 
cause,  or  at  least  not  the  only  cause,  of  the  symptoms. 

Theoretically  I  think  we  must  admit  that  no  two  causes  in 
the  world  could  be  substituted  for  each  other  and  leave  pre- 
cisely the  same  results  everywhere  ;  and  therefore  to  a  perfect 
intelligence  dealing  with  perfect  data  there  would  be  no  such 
thing  as  a  plurality  of  possible  causes.  I  think  we  must 
admit,  too,  that  in  many  cases  where  we  seem  to  be  confronted 
by  such  a  plurality  of  possible  causes  the  difficulty  is  due  to 
careless  and  avoidable  inaccuracy  ;  but,  on  the  other  hand,  I 
think  it  cannot  be  doubted  that  in  most  cases  the  difficulty  is 
due  to  the  fact  that  in  this  practical  world  we  learn  a  great 
many  things  vaguely  before  we  learn  anything  accurately  ;  so 
that  when  any  particular  question,  such  as  the  cause  of  indi- 
gestion, arises  we  cannot  expect  anybody  to  know  everything 


270   THE  METHODS   OF   DIFFERENCE   AND   AGREEMENT. 

else  so  well  that  he  can  distinguish  the  relevant  antecedents 
and  consequents  from  the  irrelevant.  In  a  purely  hypo- 
thetical case  a  person  might  be  supposed  to  know  that  his 
indigestion  after  breakfast  had  absolutely  nothing  to  do  with 
the  supper  he  ate  the  evening  before,  or  with  the  soundness 
of  his  sleep  during  the  night,  or  with  what  he  read  in  the 
morning  newspaper,  and  so  on  ;  and  yet  not  to  know  what 
really  did  cause  it.  But  in  most  actual  cases  the  facts  are 
reversed  and  we  have  to  know  what  caused  the  trouble  before 
we  can  find  out  what  circumstances  were  irrelevant — \ve  can- 
not state  our  problem  with  refinement  until  we  have  solved 
it.  And  so  '  the  characteristic  imperfection  '  of  the  method 
of  agreement  remains.  We  can  only  say  that  the  more  we 
know  to  begin  with  and  the  more  carefully  we  distinguish 
slight  differences,  the  less  trouble  it  will  give. 

Let  us  now  compare  inferences — whether  drawn  by  the 
method  of  difference  or  by  that  of  agreement — which  are 
Two  kinds  based  upon  the  comparison  of  two  changeless  sit- 
pared?C°m"  uations  with  those  which  are  based  upon  the  ob- 
servation of  changes  taking  place  in  one. 

One  advantage  in  having  a  changing  situation  when  we 
are  seeking  for  causal  relations  is  that  it  sometimes  enables  us, 
though  not  always,  to  distinguish  between  causes  and  effects. 
If  we  find  one  place  where  the  soil  is  moist  and  vegetation 
luxurious,  and  another  where  moisture  and  vegetation  are 
both  absent,  we  cannot  say  whether  the  moisture  causes  the 
vegetation  or  the  vegetation  the  moisture ;  but  when  we 
notice  things  begin  to  grow  after  a  rain  we  can  be  quite  sure 
that  in  this  case  at  least  the  growth  of  the  vegetation  is  not 
the  cause  and  the  moisture  the  effect.  If  either  of  them  is 
the  cause  of  the  other,  it  is  the  moisture.  In  comparing  two 
changeless  situations  we  talk  of  antecedents  and  consequents 
just  as  we  do  in  speaking  of  changes  ;  but  here  the  words 
are  used  rather  metaphorically,  '  antecedent  '  meaning  one  of 
a  group  of  causes,  and  '  consequent  '  one  of  a  group  of 
effects ;  and  we  cannot  tell  which  of  two  circumstances 


TWO   KINDS   OF   DATA   COMPARED.  271 

should  be  called  the  'antecedent '  and  which  the  '  conse- 
quent '  until  we  have  found  out  in  some  indirect  way  which 
of  the  two  is  cause  and  which  effect.  Where  there  is  a  change 
we  can  often  see  directly  which  event  is  antecedent,  and 
therefore  cause,  and  which  is  consequent,  and  therefore  effect. 
Yet  this  advantage  in  reasoning  from  a  changing  situation 
is  rather  dubious,  so  long  at  least  as  we  are  mere  observers. 
Often  we  notice  a  situation  changing  without  being  able  to 
tell  which  element  in  it  changes  first.  We  feel  the  breeze 
ari>ing  and  see  the  aspen  leaves  begin  to  quiver  or  the  trees 
begin  to  sway.  But  do  we  really  observe  which  came  first? 
Can  we  prove  by  direct  observation  alone  that  the  breeze 
really  came  first  and  was  therefore  the  cause — and  not  the 
effect,  as  children  sometimes  suppose — of  the  fan-like  swaying 
of  the  trees  ?  It  is  only  when  there  are  a  number  of  inter- 
mediate links  in  the  chain  that  the  interval  in  time  between 
causes  and  effects  is  really  perceptible.  Then,  again,  the 
observation  of  the  apparent  order  in  time  often  positively  leads 
us  astray.  Is  the  sound  of  thunder  caused  by  the  flash  of  light 
because  we  hear  it  afterwards  ?  Does  the  falling  of  the  ba- 
rometer cause  rain  because  it  precedes  it  ?  The  fact  is  that 
observation  of  the  order  in  time  docs  not  help  us  to  tell  which 
of  two  events  is  the  cause  and  which  is  the  effect  nearly  so  much 
as  does  a  knowledge  of  other  causal  relations.  We  do  not 
believe  that  the  wind  moves  the  trees,  and  not  the  trees  the 
wind,  because  we  see  that  the  wind  comes  first,  but  rather 
because  we  do  not  know  anything  but  wind  that  is  likely  to 
move  the  trees,  while  we  do  kno\v  something  besides  the  trees 
that  can  stir  up  the  wind.  One  theory  leaves  a  broken 
causal  chain  and  the  other  does  not.  In  other  words,  a  state 
of  affairs  in  which  the  wind  moves  the  trees  fits  into  the  rest 
of  the  world  as  we  know  it  better  than  one  in  which  the 
movement  of  the  trees  causes  the  wind;  and  so  we  assume 
that  the  former  state  of  affairs  and  not  the  latter  is  the  real 
one.  But  such  reasoning  as  this  is  quite  as  applicable  to 
cases  in  which  there  is  not  any  change  as  to  those  in  which 


272   THE  METHODS   OF  DIFFERENCE  AND   AGREEMENT. 

there  is.  Thus  this  advantage  which  reasoning  about  change 
seems  to  possess  over  reasoning  about  situations  which  do  not 
change  is  often  only  apparent. 

When  we  assume  that  one  event  must  be  the  effect  of  an- 
other merely  because  it  follows  it — ' post  hoc  ergo propter  hoc  ' 
— we  commit   a  very  common  blunder,    which 
ergo  propter   is  sometimes  called  the  fallacy  of  '  False  Cause  ', 
toc'  but  is  more  commonly  designated  by  the  Latin 

phrase  which  describes  the  reasoning. 

Whether  the  cases  compared  compel  us  to  draw  our  infer- 
ences by  the  method  of  agreement  or  by  the  method  of  dif- 
ference, and  whether  we  are  comparing  two  dif- 
Advantages      ..  . 

of  expert-  ferent  situations  or  the  changes  in  one,  are  not 
meat.  ,  .. 

nearly  so  important  questions  as  one  not  yet  men- 
tioned. This  is  the  question  whether  we  merely  observe  and 
compare  situations  as  we  happen  to  find  them  or  whether  we 
deliberately  create  them  for  the  purpose  of  answering  specific 
questions  :  the  question  whether  our  inference  is  based  upon 
mere  '  observation  '  or  upon  '  experiment '. 

Mere  observation  often  raises  problems ;  but  when  they 
are  once  raised,  experiment,  where  it  can  be  tried  properly, 
gives  the  more  satisfactory  answers. 

In  the  first  place,  the  very  object  of  experiment  is  to  pro- 
duce conditions  which  are  thoroughly  understood  and  from 
which  all  disturbing  factors  are,  so  far  as  possible,  removed. 
Hence  when  we  experiment  there  is  much  less  chance  that 
some  real  cause  has  been  overlooked  than  when  we  merely 
observe  some  of  the  occurrences  that  take  place  amidst  the 
great  confusion  of  natural  conditions. 

A  second  point  in  favor  of  experiment  is  that  it  enables  us 
to  tell,  as  observation  does  not,  not  merely  that  a  pair  of  cir- 
cumstances have  some  direct  or  indirect  causal  relation,  but 
that  one  is  the  actual  cause  of  the  other,  and  which  one  that  is. 

We  have  just  seen  (p.  271)  how  these  questions  can  often 
be  settled  indirectly,  through  our  knowledge  of  the  rest  of  the 
world.  Experiment  often  enables  us  to  settle  them  directly. 


ASSUMPTION   IN   EXPERIMENT.  273 

If  I  blow  air  against  the  branches  of  a  tree,  they  will  begin 
to  move ;  and  from  this  I  conclude  that  in  this  case  at  least 
the  movement  of  the  air  is  the  cause  and  the  movement  of  the 
tree  the  effect.  On  the  other  hand,  if  I  sway  a  tree,  a  little 
breeze  will  arise  ;  and  from  this  I  conclude  that  in  this  case 
the  movement  of  the  tree  is  the  cause,  and  the  movement  of 
the  air  the  effect.  So  I  say  that  either  may  cause  the  other. 
Again,  if  I  heat  the  air  around  a  thermometer,  I  will  find  the 
mercury  rise ;  but  if  I  raise  the  mercury  in  some  other  way,  I 
will  not  find  any  noticeable  change  in  the  temperature  of  the 
surrounding  air ;  so  I  conclude  that  the  temperature  affects  the 
height  of  the  mercury,  but  not  vice  versa.  Still  again,  if  I 
forcibly  lower  the  mercury  in  a  barometer,  a  storm  will  not 
follow;  and  if  I  make  a  little  rainstorm  around  it  with  a 
watering-pot  without  lowering  its  temperature,  the  mercury 
will  not  fall.  So  I  conclude  that  the  fall  of  the  mercury  does 
not  cause  the  rain,  or  the  rain  the  fall  of  the  mercury,  but 
that  when  the  two  are  found  together  they  must  be  joint 
effects  of  the  same  cause  ;  and  if  I  guess  what  that  cause  is,  I 
may  be  able  to  verify  my  guess  by  a  new  set  of  experiments 
designed  to  test  the  relative  weights  of  air  and  watery  vapor, 
and  the  effect  produced  upon  the  mercury  in  a  barometer  by 
the  pressure  of  such  different  weights. 

We  can  reach  all  these  conclusions  by  experiment  because 
we  take  for  granted  the  relative  spontaneity  of  our  own  vol- 
untary acts.      It  may  be  that  we  ourselves  are  as 

..  .  .  .  .     ,         Assumption. 

much  a  part  of  nature  as  anything  else  and  that   inexperi- 

every  one  of  our  acts  is  the  necessary  effect  of 
some  preceding  cause.  But  we  assume  that  we  know  enough 
about  ourselves  to  be  sure  that  the  immediate  causes  of  our 
acts  are  very  different  from  the  immediate  causes  of  such 
things  as  wind,  temperature,  and  rain.  If  we  did  not  make 
this  assumption,  we  should  have  to  assume  that  our  own  acts 
in  various  experiments  and  the  results  which  seem  to  follow 
from  them  might  be  merely  joint  effects  of  the  same  causes. 
Hence  we  could  not  be  sure  that  our  blowing  of  the  air  made 


274   THE   METHODS   OF   DIFFERENCE  AND   AGREEMENT. 

the  tree  move,  or  that  our  squeezing  of  the  bulb  or  our  heating 
of  the  air  around  it  raised  the  mercury  in  the  thermometer. 
For  unless  we  assume  our  own  relative  independence  it  might 
well  be  that  there  was  some  general  state  of  affairs  which  made 
the  tree  sway  and  at  the  same  time  made  our  brain-cells  dis- 
charge and  our  muscles  contract  as  though  we  were  swaying 
it ;  and  so  with  the  other  examples.  On  the  other  hand,  if 
our  voluntary  acts  are  spontaneous  so  far  as  the  events  which 
we  are  investigating  are  concerned, — if  they  are  never  mere 
effects  of  preceding  events  in  the  series  under  consideration, — 
then,  though  these  voluntary  acts  and  the  changes  around  us 
which  follow  them  may  sometimes  coincide  through  mere 
chance,  they  can  never  be  joint  effects.  If  there  is  any 
causal  relation  between  them  at  all,  the  voluntary  acts  must 
be  the  causes,  and  the  changes  that  follow  must  be  their 
effects.* 

*  A  third  advantage  connected  with  experiment  is  that  inferences 
based  upon  it  are  accompanied  with  a  greater  feeling  of  satisfaction. 
The  feeling  of  muscular  exertion  which  comes  with  our  own  acts  is  as- 
sociated very  closely  in  the  minds  of  most  people  with  the  idea  of  cause 
and  effect  or  is  really  a  part  of  it.  Consequently  the  actual  production 
of  an  effect  by  our  own  exertion  seems  to  give  an  immediate  feeling  of 
the  causal  connection  that  nothing  else  can  give. 


CHAPTER    XXVII. 
THE  JOINT   METHOD   OF    AGREEMENT  AND   DIFFERENCE. 

FOR  a  perfect  application  of  the  Method  of  Difference,  as 
we  have  seen,  there  must  be  two  cases  alike  in  every  respect 

except  that  in  one  a  certain  effect  and  its  cause 

.      i  j  c  r  i-       •  c   Its  function, 

are  both  present  ;  and  for  a  perfect  application  of 

the  Method  of  Agreement  there  must  be  two  cases  different 
in  every  respect  except  that  the  causally  related  circum- 
stances are  present  (or,  it  might  be,  absent)  in  both.  More- 
over there  is  always  danger  that  the  method  in  question  has 
not  been  applied  perfectly,  because  of  the  possible  presence 
of  other  points  of  difference  or  resemblance  which  have  not 
been  noticed.  But  suppose  that  other  points  of  difference  or 
resemblance  are  present  and  are  noticed,  and  that  we  cannot 
find  any  two  cases  in  which  they  are  not ;  is  inference  no 
longer  possible  ? 

It  is  not  possible  if  there  are  only  two  such  cases ;  but  if 
there  are  more  and  they  differ  widely  from  each  other,  it  may 
be.  Suppose,  for  example,  that  we  have  all  the  following 
combinations,  the  letters  from  A  to  M  standing  for  known 
antecedents,  the  letters  from  N  to  Z  for  known  consequents, 
and  the  blanks  for  other  possible  but  unknown  antecedents 
and  consequents. 

1)  ABCDEF-NOPQRS-        4)  BCDE-OPQR- 

2)  ABGHI-NOTUV-  5)  CFGH-PSTU- 

3)  ACGKL-NPTXY-  6)   EHIJKL-RUVWXY- 

275 


276  JOINT   METHOD   OF   AGREEMENT   AND   DIFFERENCE. 

We  notice  that  where  A  is  present  N  is  present,  and  that 
where  A  is  absent  N  is  absent  (which  is  the  same  thing  as 
saying  that  where  A  is  present  N  is  present,  and  where  N  is 
present  A  is  present);  and  this  suggests  that  A  is  the  cause 
of  N.  But  how  shall  we  prove  it?  The  Method  of  Differ- 
ence is  inapplicable,  because  there  are  no  two  cases  (not 
even  the  first  and  the  fourth)  that  differ  in  no  respect  except 
the  presence  of  A  and  N  in  one  case  and  their  absence  in  the 
other.  In  the  same  way  there  are  no  two  cases  from  which 
we  can  prove  the  connection  by  the  Method  of  Agreement. 

Yet  there  is  a  way  in  which  the  Method  of  Agreement  can 
be  applied,  and  applied  doubly.  Assuming  that  the  cause  of 
N  is  to  be  found  amongst  the  observed  antecedents  and  that  it 
is  always  the  same,  we  can  prove  from  the  first  two  cases 
that  it  is  either  A  or  B  or  the  combination  AB,  for  A  and  B 
are  the  only  conditions  present  in  both.  From  the  first  and 
third  cases  we  can  prove  in  the  same  way  that  the  cause  is 
either  A  or  C  or  AC  ;  and  from  the  second  and  third  that 
it  is  either  A  or  G  or  AG.  And  if,  as  we  have  assumed,  the 
cause  is  the  same  in  all  the  cases,  it  must  be  A.  Thus,  though 
the  presence  of  A  and  N  is  not  the  only  respect  in  which  any 
two  cases  agree,  it  is  the  only  known  respect  in  which  all  the 
three  positive  cases  agree,  and  A  is  therefore  the  cause  of  N,  if 
the  cause  of  N  is  always  the  same  observed  circumstance. 
This  is  a  perfectly  legitimate  application  of  the  Method  of 
Agreement;  but,  like  all  applications  of  that  method,  it  is 
subject  to  the  objections  that  the  cause  of  N  may  not  be  the 
same  in  all  cases,  and  then  even  if  it  is,  the  real  cause  may 
be  some  unknown  circumstance,  represented  by  one  of  the 
blanks. 

The  Method  of  Agreement  can  be  applied,  again,  to  the 
negative  cases  4,  5,  and  6.  These  all  agree  in  the  absence 
of  A  and  N,  and  if  instead  of  only  three  relatively  simple 
cases  we  had  a  great  number  that  were  quite  complex  (as  we 
often  have  in  Nature),  we  might  be  inclined  to  say  that  the 
absence  of  A  and  N  was  the  only  respect,  or  rather  the  only 


ITS  FUNCTION.  277 

respect  worth  considering,  in  which  all  these  cases  do  agree. 
In  this  way  we  might  have  a  double  assurance,  one  from  the 
positive  cases  and  one  from  the  negative,  that  A  was  the  cause 
of  N.  The  negative  cases  have  this  advantage  :  inference 
based  upon  them  is  not  subject  to  the  objection  arising  from 
the  plurality  of  possible  causes.  If  the  absence  of  A  is  always 
accompanied  by  the  absence  of  N  whether  any  other  ante- 
cedent is  absent  or  not,  then  A  not  only  may  be  the  cause  of 
N,  but  must  be  ;  and  it  must  also  be  the  only  possible  cause. 
On  the  other  hand  the  negative  cases  are  subject  to  the  tre- 
mendous disadvantage  that  it  is  practically  impossible  to 
prove  a  negative,  to  show  that  a  pair  of  given  circumstances 
are  the  only  ones  which  can  not  be  found  in  any  of  the  cases. 
Consequently,  when  negative  cases  are  taken  by  themselves 
they  are  much  more  dangerous  to  work  with  than  positive. 
Yet  so  far  as  they  go  they  tend  to  confirm  the  results  based 
upon  the  positive  cases,  and  they  suggest  at  least  that  in  all 
the  cases  observed  there  was  only  one  cause.  Because  results 
based  upon  negative  instances  of  this  sort  can  be  regarded 
as  confirming  those  based  on  the  positive,  the  employment 
of  the  two  is  called  by  Fowler*  the  Double  Method  of 
Agreement. 

But  these  positive  and  negative  instances  can  be  looked  at 
from  another  standpoint,  and  regarded  as  data  for  an  indirect 
application  of  the  method  of  difference.  We  can  say:  ''When 
N  is  present  and  every  condition  but  A  can  be  varied  without 
causing  its  disappearance,  these  conditions  are  necessarily 
immaterial.  In  the  same  way  when  every  condition  but  the 
absence  of  A  can  be  varied  without  causing  its  appearance, 
these  conditions  also  are  immaterial.  But  the  distinction  be- 
tween immaterial  conditions  may  be  ignored  ;  therefore  the 
only  important  distinction  between  the  two  sets  of  cases  is  that 
in  the  one  A  and  N  are  both  present,  and  in  the  other  they 
are  both  absent. '  And  this  is  all  we  need  for  the  method  of 

*  "  Inductive  Logic  ",  Macmilhn,  1889. 


2 78" JOINT   METHOD   OF   AGREEMENT   AND   DIFFERENCE. 

difference.  Hence  the  double  method  is  called  by  Mill  the 
Indirect  Method  of  Difference.  Because  the  method  of  agree- 
ment and  the  method  of  difference  are  both  involved  it  is  also 
called  by  him  the  Joint  Method  of  Agreement  and  Difference. 

Mill's  canon  for  the  method  is  this : 

"  If  'two  or  more  instances  in  which  the  phenomenon  occurs 
have  only  one  circumstance  in  common,  while  tiuo  or  more  in- 
stances in  which  it  does  not  occur  have  nothing  in  common  save  ^ 
the  absence  of  that  circumstance,  the  circumstance  in  which 
alone  the  two  sets  of  instances  differ  is  the  effect,  or  the  cause, 
or  an  indispensable  part  of  the  cause,  of  tlie  phenomenon." 

"  This  method",  Mill  says,  "  may  be  called  the  Indirect 
Method  of  Difference,  or  the  Joint  Method  of  Agreement 
Compared  ar>d  Difference;  and  consists  in  a  double  employ  - 
method1'  ment  of  the  Method  of  Agreement,  each  proof 
difference.  being  independent  of  the  other  and  corroborat- 
ing it.  But  it  is  not  equivalent  to  a  proof  by  the  direct 
Method  of  Difference.  For  the  requisitions  of  the  Method 
of  Difference  are  not  satisfied  unless  we  can  be  quite  sure 
either  that  the  instances  affirmative  of  a  [i.e.,  N,  the  con- 
sequent in  question]  agree  in  no  antecedent  whatever  but 
A  [the  antecedent  in  question],  or  that  the  instances  nega- 
tive of  a  agree  in  nothing  but  the  negation  of  A.  Now, 
if  it  were  possible,  which  it  never  is,  to  have  this  assurance, 
we  should  not  need  the  joint  method  ;  for  either  of  the  two 
sets  of  instances  separately  would  then  be  sufficient  to  prove 
causation.  This  indirect  method,  therefore,  can  only  be  re- 
garded as  a  great  extension  and  improvement  of  the  Method 
of  Agreement,  but  not  as  participating  in  the  more  cogent 
nature  of  the  Method  of  Difference."  * 

Mill  is  right  in  saying  that  the  Joint  Method  will  not  give 
absolute  certainty.  But  then  neither  will  the  Method  of  Dif- 
ference, applied  in  our  common  human  ignorance  of  a  vast 
number  of  surrounding  conditions.  A  theoretically  perfect 

*  "Lo^ic",  15k.  Ill,  Chap.  VIII,  See.  4. 


COMPARED  WITH  SIMPLE  METHOD  OF  DIFFERENCE.    279 

application  of  the  Method  of  Difference  will  give  a  theoret- 
ically perfect  proof;  but  none  of  our  applications  of  the 
method  are  theoretically  perfect,  and  a  good  many  of  them 
are  not  practically  perfect  either.  Mill  and  other  writers  on 
logic  tell  us  that  experiments  are  usually  based  upon  the 
Method  of  Difference  and  that  that  is  one  reason  why  experi- 
ment is  better  than  mere  observation.  It  is  true  that  they  are 
based  on  that  method  in  any  single  experiment, — we  add  one 
new  circumstance  and  see  if  the  effect  in  question  follows. 
But  why  are  the  conclusions  based  on  experiment  sometimes 
erroneous  ?  Why  do  scientists  all  over  the  world  try  to  re- 
peat and  thus  'verify  '  each  others'  experiments,  if  any  one 
could  be  sure  that  the  method  was  rigorously  applied  the  first 
time  ?  The  fact  of  the  matter  is  that  in  all  cases  where 
experiment  is  possible,  whether  in  common  life  or  in  science, 
the  final  appeal  is  not  usually  to  the  Method  of  Difference, 
but  to  the  Joint  Method.  I  destroy  a  frog's  brain,  suspend 
the  creature  by  the  nose,  and  dip  its  foot  into  a  solution  of 
acid  ;  and  a  second  or  two  later  I  see  the  foot  lifted  out  of 
the  acid  just  as  if  the  brainless  frog  knew  what  it  was  doing. 
By  the  Method  of  Difference  I  reason  that  the  contact  with 
the  acid  was  what  made  the  frog  lift  the  foot  up.  But  am  I 
satisfied  with  this  one  experiment  ?  If  such  an  occurrence 
happens  to  be  unfamiliar  and  I  am  really  interested  in  the 
question,  will  I  not  try  the  experiment  again  under  as  many 
different  conditions  as  I  can  think  of,  and  ask  others  to  do  the 
same?  And  if  everybody  gets  the  same  result,  will  they  not 
then  have  two  groups  of  cases  to  compare,  the  members  of 
each  group  varying  in  as  many  respects  as  possible  except  the 
two  in  question?  In  one  group  there  are  all  the  cases  in 
which  the  foot  has  not  yet  touched  the  acid  and  has  not  been 
drawn  up;  in  the  other  are  all  the  cases  in  which  the  foot  has 
touched  the  acid  and  has  been  drawn  up.  And  these  are  the 
kind  of  data  to  which  we  apply  the  Joint  Method. 

In    conditions    known    to    be    theoretically    perfect    one 
experiment  based  on   the  Method   of   Difference  would   be 


280  JOINT   METHOD   OF   AGREEMENT   AND   DIFFERENCE. 

sufficient  to  give  absolute  proof  of  a  causal  relation;  but 
because  there  are  always  a  great  many  possible  sources  of 
error,  we  can  always  feel  surer  of  conclusions  when  the 
experiments  upon  which  they  are  based  have  been  performed 
many  times  under  different  conditions  than  when  they  have 
been  performed  only  once.  And  thus  even  where  the 
Method  of  Difference  is  most  applicable  we  appeal  from  it 
to  the  Joint  Method. 


CHAPTER   XXVIII. 

COUNTERACTING    AND    COMPLEX    CAUSES. 

WE  have  reasoned  thus  far  on  the  assumption  that  an 
adequate  cause  is  invariably  accompanied  by  its  effect. 
We  have  virtually  said :  '  The  effect  may  be  present  with- 
out this  particular  cause,  because  the  same  effect  counteract- 
may  be  due  to  any  one  of  several  causes;  but  In8:causes- 
that  does  not  imply  that  the  cause  can  be  present  without 
its  effect,  and  if  what  we  supposed  to  be  a  cause  of  a  given 
effect  is  ever  found  to  be  present  without  the  effect,  we  were 
mistaken  in  supposing  it  was  the  cause  (though  it  might  have 
been  part  of  the  cause).  If  A  causes  N,  N  may  sometimes 
be  present  without  A,  but  A  can  never  be  present  without  N. ' 
This  is  the  principle  on  which  we  have  been  reasoning  up 
to  the  present,  and  if  we  were  in  a  world  in  which  nothing 
else  could  '  come  between  '  A  and  N,  or  affect  their  relations 
to  each  other,  reasoning  based  on  this  principle  would 
always  be  correct.  As  it  is,  it  is  not.  It  may  be  that  A  is 
a  perfectly  adequate  cause  of  N  and  yet  that  it  is  sometimes 
present  without  N.  In  the  presence  of  a  '  Counteracting 
Cause'  a  cause  perfectly  adequate  in  itself  will  fail  of  its 
effect.  The  swift  current  of  a  river  causes  things  floating  in 
it  to  drift  down  the  stream;  and  yet  if  there  is  a  hurricane 
blowing  in  the  opposite  direction,  the  things  may  drift  up 
and  not  down.  The  working  of  the  engines  makes  the  ship 
move;  but  now  she  is  fast  on  the  rocks  and  for  all  their 
work  the  engines  cannot  move  her. 

281 


282          COUNTERACTING   AND   COMPLEX   CAUSES. 

Without  going  into  any  theoretical  discussion,  the  prac- 
tical lesson  to  draw  from  such  cases  is  this:  There  is  a  differ- 
ence between  saying  that  a  cause  always  produces  its  natural 
effects  and  saying  that  it  always  tends  to  produce  them;  and 
this  latter  is  all  we  have  a  right  to  say.  Put  more  concretely, 
this  rule  means  that  if  we  are  searching  for  the  cause  of  a 
given  effect  N  and  find  that  A  is  sometimes  present  when  N 
is  not,  we  must  not  conclude  from  this  that  A  is  not  the 
cause  of  X,  until  we  are  sure  that  there  is  nothing  present 
which  can  counteract  A's  effect. 

If  we  know  what  can  counteract  the  effect  of  A,  or,  what 
amounts  in  this  case  to  the  same  thing,  what  can  prevent 
the  production  of  X,  our  task  of  discovering  the  relation 
between  A  and  X  will  be  easy  enough.  But  if  we  do  not 
know  enough  about  either  A  or  X  to  say  what  would  preven* 
the  one  from  causing  the  other,  then  our  task  will  be  very 
much  more  difficult.  If  A  and  X  occur  together  often 
enough  to  make  us  suspect  that  A  is  really  a  cause  of  X", 
though  sometimes  counteracted  in  its  working  by  G,  H,  or 
j,  we  must  simply  leave  the  matter  doubtful  until  we  can 
make  or  find  conditions  simple  enough  or  varied  enough  to 
let  us  infer  something  about  the  real  nature  of  some  of  these 
influences. 

Sometimes  a  situation  may  be  so  complicated  that  we  have 
to  deal  not  only  with  several  kinds  of  causes  and  counter- 
acting causes,  but  with  still  other  antecedents  that  counteract 
the  counteracting  causes.  But  however  complicated  our 
problem  may  be,  the  principle  of  exclusion  upon  which  we 
must  depend  for  its  solution  remains  the  same. 

The  possibility  of  counteracting  causes  makes  it  possible 
to  commit  a  blunder  of  precisely  the  opposite  kind  from  that 
made  possible  by  the  plurality  of  possible  causes.  If  we 
forget  that  practically  the  same  effect  can  be  produced  by 
any  one  of  several  causes,  we  may  assert  that  something  is 
the  cause  of  this  effect,  when  it  is  not  the  cause  at  all,  simply 
because  it  happens  to  be  the  only  one  thing  present  in  all 


CAUSES    'COMPOUNDED'   OR    'COMBINED.'  283 

the  cases  we  have  observed.  On  the  other  hand,  if  we  forget 
that  a  cause  is  sometimes  counteracted,  we  may  deny  that 
something  is  the  cause,  when  it  really  is,  because  it  is  some- 
times present  without  the  effect.  Thus,  if  we  are  careless, 
the  presence  of  a  plurality  of  causes  may  make  us  find  false 
causes,  and  the  presence  of  a  counteracting  cause  may  make 
us  overlook  true  ones. 

Methods  of  investigating  causal  relations  have  been  dis- 
cussed thus  far  as  though  we  assumed  that  every  effect  had 
some  one  simple  cause  and  every  cause  some  one 
simple  effect.      But  it  often  happens  that  several  pounded 'or 
causes  act  together  to  produce  a  given  effect  and 
that  there  is  some  reason  why  we  should  not  regard  them  as 
one. 

There  are  two  ways  in  which  causes  can  act  together 
to  produce  a  joint  effect.  Sometimes  the  effect  of  each  one 
of  them  separately  is  like  that  of  each  of  the  others  and  like 
that  of  the  group  as  a  whole.  Sometimes  the  separate  effect 
of  each  is  unlike  the  effect  of  each  of  the  others,  and  the 
effect  of  all  together  is  unlike  the  effect  of  any  one.  Here 
is  a  case  of  the  first  sort.  The  amount  of  money  that  a  man 
has  at  the  end  of  the  year  depends  upon  how  much  he  had 
to  start  with,  what  he  made  or  lost  each  day  in  his  regular 
business,  what  he  made  or  lost  in  other  ways,  what  he  spent 
for  regular  household  purposes,  what  he  spent  for  amuse- 
ment, what  he  gave  away.  In  his  cash  account  he  sets  down 
all  the  expenditures  on  one  page  and  all  the  receipts  on 
another,  adds  all  the  items  on  the  same  page  together,  and 
subtracts  them  from  the  total  of  the  other  page.  In  his 
balance  it  makes  absolutely  no  difference  what  the  money 
that  he  spent  was  spent  for.  If  he  wants  a  certain  balance 
and  finds  before  the  end  of  the  year  that  he  is  spending  too 
much  for  rent  and  groceries,  he  may  make  up  for  it  by 
cutting  down  his  expenditures  for  recreation  and  charity. 
All  the  forces  dealt  with  in  mechanics  are  causes  of  this  sort. 
When  one  is  '  added  to  '  or  '  subtracted  from  '  another  the 


284          COUNTERACTING   AND   COMPLEX   CAUSES. 

result  is  precisely  the  same  as  it  would  have  been  if  the  body 
on  which  they  are  acting  had  been  acted  upon  by  only  one 
force  equal  to  the  sum  or  the  difference.  In  mechanics  we 
speak  of  the  '  Composition  of  Forces  ' ;  and  Mill  paraphrases 
the  term  and  speaks  of  the  '  Composition  of  Causes  '  when 
the  effect  of  them  all  can  be  considered  in  this  way  as  the 
algebraic  sum  of  the  effects  of  each  of  them.  The  separate 
causes  and  effects  which  are  thus  added  together  he  speaks 
of  as  '  Compounded  '. 

Now  for  the  second  kind  of  joint  effects.  To  raise  a  crop 
of  onions  there  must  be  seeds,  air,  moisture,  warmth,  and 
soil.  If  any  one  of  these  is  left  out,  the  result  is,  not  smaller 
onions  or  fewer  onions,  but  no  onions  at  all.  Moreover  if 
a  farmer  finds  that  his  onions  are  getting  too  much  heat  from 
the  sun,  he  cannot  even  things  up  by  giving  them  so  much 
less  water.  In  the  same  way  if  a  cook  finds  that  she  has  put 
too  much  sugar  into  her  cake,  she  cannot  improve  matters 
by  leaving  out  the  flour.  Cooking  is  a  matter  of  chemistry, 
and  chemistry  is  full  of  examples  of  this  kind  of  joint  effects. 
Oxygen  and  hydrogen  '  combine '  to  form  water,  whose 
appearance  and  action  are  quite  different  in  almost  every 
respect  from  those  of  either  of  them.  In  the  same  way  the 
green  poisonous  gas  chlorine  '  combines  '  with  the  very 
different  yellowish  metal  sodium  to  form  common  salt,  which 
again  is  very  different  from  either  of  them.  Joint  effects 
which  differ  in  this  way  from  the  effects  of  any  of  the  causes 
separately  are  called  '  Heteropathic  ',  and  since  the  effect 
of  uniting  the  causes  is  like  that  of  making  a  chemical 
'  combination  '  the  causes  are  said  to  be  '  Combined  '. 

To  produce  heteropathic  or  combined  effects  it  is  neces- 
sary that  the  causes  concerned  should  all  be  present  at  the 
same  time  or  follow  each  other  in  some  fixed  order.  If  the 
onion  seed  is  to  grow,  it  must  be  warmed  and  moistened  after 
it  is  put  in  the  soil,  not  before;  if  the  cake  is  to  taste  right, 
its  various  ingredients  must  be  mixed  before  it  is  cooked, 
not  afterwards.  To  produce  compound  effects  this  is  not 


CAUSES    'COMPOUNDED'    OR    'COMBINED.'  285 

necessary.  The  onions  weigh  as  much  whether  they  are  all 
thrown  into  the  basket  at  once  or  one  after  the  other;  the 
ingredients  of  the  cake  cost  as  much  whether  they  are  all 
purchased  at  the  same  time  or  at  different  times.  The 
'  parallelogram  of  forces  '  in  physics  is  a  graphic  way  of 
explaining  that  when  a  body  that  can  move  freely  is  acted 
upon  by  several  forces  at  once  it  reaches  the  same  point 
(though  it  travels  along  a  diagonal)  as  it  would  have  reached 
if  it  had  been  acted  upon  by  the  same  forces  one  after  the 
other. 

Because  mathematics  can  be  applied  freely  in  calculating 
the  joint  effect  when  causes  are  '  compounded  '  but  cannot 
be  so  applied  when  they  are  '  combined  ',  we  have  made  a 
distinct  advance  in  knowledge  when  we  can  say  beforehand 
in  which  way  they  will  be  conjoined.  For  example,  it  is  a 
great  advantage  if  we  can  be  sure  that  the  weight  of  a  com- 
pound, however  formed,  is  always  equal  to  the  compounded 
weight — i.e.,  to  the  sum  of  the  weights — of  its  ingredients. 
According  to  an  old  story  the  Royal  Society  was  once  tricked 
into  discussing  the  question  why  it  was  that  nothing  is  added 
to  the  weight  of  a  vessel  of  water  when  a  live  fish  is  put  into 
it;  and  the  discussion  of  one  explanation  after  another  went 
on  for  a  long  time  before  any  one  suggested  that  they  try  the 
experiment  and  see  whether  what  they  were  trying  to  explain 
was  really  the  case.  The  moral  naturally  attached  to  the 
story  is  that  it  is  wise  to  find  out  whether  a  fact  exists  before 
you  try  to  explain  it;  but  here  it  is  used  to  illustrate  some- 
thing else.  If  any  one  were  quite  sure  that  the  weight  of 
any  body  is  a  compound  effect  made  up  of  the  weight  of  all 
its  separate  parts,  he  would  not  think  it  necessary  to  try  the 
experiment  at  all.  He  could  be  sure  beforehand  that  an 
addition  of  any  kind  to  the  contents  of  the  vessel  would 
increase  its  weight,  and  he  would  know  that  whether  the  fish 
put  into  it  were  alive  or  dead  could  make  no  possible  differ- 
ence. If  the  Royal  Society  ever  did  seriously  discuss  such 
a  question  as  this,  it  must  have  been  when  physicists  were 


2«6          COUNTERACTING   AND   COMPLEX   CAUSES. 

not  all  certain  that  weight  is  a  compound  effect  and  never 
under  any  circumstances  or  to  any  extent  heteropathic. 

The  distinction  between  'compounded'  and  'combined' 
causes  can  be  applied  quite  as  well  when  some  of  the  causes 
tend  to  counteract  the  effects  of  the  others  as  when  they  all 
assist  each  other. 

A  counteracting  cause  of  the  '  combined '  sort  simply 
breaks  up  or  nullifies  the  combination  that  would  otherwise 
have  produced  the  effect  in  question.  If  somebody  puts 
out  the  chemist's  fire  and  does  it  soon  enough,  the  combina- 
tion which  he  expected  will  not  occur.  If  a  man  quarrels 
with  his  employer  and  loses  his  place,  or  if  the  employer  fails 
and  cannot  pay  the  man  for  his  work,  the  quarrel  or  the 
failure  is  not  a  kind  of  expenditure  that  tends  according  to 
its  amount  to  counteract  the  effect  of  the  man's  earnings. 
It  puts  an  end  to  his  earnings  altogether.  The  effect  of 
these  counteracting  causes  is  '  heteropathic  '. 

A  counteracting  cause  of  the  '  compounded  '  sort  simply 
adds  a  negative  result  to  the  positive  one  produced  by  the 
causes  that  it  is  said  more  or  less  to  counteract;  and  conse- 
quently in  calculating  the  net  result  we  have  merely  to  sub- 
tract one  set  of  results  from  the  other.  Thus  the  spending 
or  giving  away  of  money  tends  according  to  its  amount  to 
counteract  the  effect  of  earning  it,  and  if  we  wish  to  find  the 
gain  or  loss  during  the  year  we  have  only  to  subtract  the 
expenditures  from  the  receipts  or  vice  versa.  Here  the  effects 
are  not  '  heteropathic  ',  but  '  compounded  '. 


CHAPTER   XXIX. 

THE  METHODS   OF  RESIDUES  AND   CONCOMITANT 
VARIATIONS. 

WHEN  we  explain  any  state  of  affairs,  such  as  a  man's 
financial  balance  at  the  end  of  the  year,  as  the  '  com- 
pounded '  effect  of  a  number  of  different  causes, 

.      ,  -  ,  ,  t    Quantitative 

and  when  we  give  figures  to  show  the  amount  ot  treatment  ef 

the  total  effect  contributed  by  each,  it  is  evident 
that  we  are  dealing  with  the  question  of  causation  from  the 
quantitative  standpoint.  It  is  no  longer  a  mere  question  of 
whether  a  certain  kind  of  cause  was  present  or  not,  but  if  is 
a  question  also  of  its  precise  amount.  If  a  man's  actual 
balance  and  the  balance  shown  by  his  cash  account  do  not 
agree,  there  is  something  which  has  not  been  accounted  for, 
and  the  causal  explanation  of  his  financial  standing  is  not 
complete.  This  quantitative  treatment  of  a  question  of 
cause  and  effect  evidently  rests  on  the  assumption  that  the 
cause  of  every  event  must  be  capable  of  producing  precisely 
that  amount  of  effect,  no  more  and  no  less. 

Because  we  have  a  right  to  demand  an  explanation  for  the 
precise  amount  of  every  effect  as  well  as  for  its  quality  two 
other  methods  of  causal  inquiry  can  be  added  to  the  three 
already  considered  :  the  Method  of  Residues  and  the  Method 
of  Concomitant  Variations.  They  both  depend  upon  a 
quantitative  application  of  the  Method  of  Difference. 

For  the  Method  of  Residues  Mill  lays  down  the  following 
canon:  "  Subtract  from  any  phenomenon  such  part  as  is  known 

287 


288  METHOD  OF  RESIDUES. 

by  previous  inductions  to  be  the  effect  of  certain  antecedents,  and 
Method  of  the  residue  of  the  phenomenon  is  the  effect  of  the 
Residues.  remaining  antecedents."  If  we  know  that  a  man 
has  an  annual  income  of  $3200,  and  if  we  know  that  his 
salary  is  $2000  and  that  the  annual  dividend  on  his  railroad 
stock  is  $500,  then  we  can  infer  that  he  has  some  other 
source  or  sources  of  income  that  produce  $700  a  year. 
And  if  we  happen  to  know  that  his  only  other  source  of 
income  is  his  share  in  an  iron  company,  we  can  infer  still 
further  that  the  iron  company  pays  him  a  dividend  of  $700 
a  year,  no  more  and  no  less.  Similarly,  if  a  man  in  a  posi- 
tion of  trust,  with  a  salary  of  $1000  a  year  and  no  private 
fortune,  is  spending  $5000  a  year,  his  employer  will  have 
reason  to  suspect  that  the  man  is  stealing  or  has  stolen  from 
him  enough  to  make  the  difference.  To  take  still  another 
illustration:  Suppose  we  know  that  the  planet  Uranus  is 
acted  upon  by  the  attraction  of  the  sun  and  of  the  planets 
nearest  to  it,  Jupiter  and  'Saturn,  in  such  a  way  as  to  bring 
it  to  a  certain  place  at  a  certain  time;  and  suppose  that 
when  the  time  comes  the  planet  is  not  there:  then  we  can 
be  sure  that  if  our  previous  calculation  was  correct,  there  is 
some  other  force  acting  on  the  planet  and  that  this  force  is 
just  strong  enough  to  drag  it  from  the  place  where  the  cal- 
culation showed  that  it  ought  to  be  to  the  place  where  it 
actually  is.  By  calculating  the  strength  and  direction  of  such 
an  additional  force  acting  on  Uranus  the  planet  Neptune  was 
actually  looked  for  and  discovered. 

The  difference  between  the  Method  of  Residues  and  the 
ordinary  Method  of  Difference  does  not  lie  merely  in  the 
fact  that  the  Method  of  Residues  considers  questions  of 
quantity;  for  the  next  variation  of  the  Method  of  Difference 
that  we  are  about  to  consider  does  that  also.  It  lies  rather 
in  the  fact  that  when  we  use  the  Method  of  Difference  our 
knowledge  of  what  happens  when  the  residual  cause  is  not 
present  is  gained  from  direct  observation, — we  see  what 
happens  when  all  the  causes  except  the  one  under  investiga- 


METHOD   OF   RESIDUES.  289 

tion  are  present  together.  With  the  Method  of  Residues  we 
do  not  directly  observe  what  happens  when  all  the  causes 
except  the  one  in  question  are  present  together.  We  only 
calculate  it  from  what  we  know  of  the  way  in  which  they  act 
when  they  are  present  separately. 

The  Method  of  Residues  is  attended  in  practice  by  three 
dangers. 

The  first  danger  is  that  in  making  our  subtraction  we  may 
overlook  the  '  combined  '  or  heteropathic  effect  of  some  of 
the  causes  which  we  subtract,  and  thus  attribute  too  much 
to  the  remaining  causes.  For  example,  three  persons.  A,  B, 
and  C,  are  in  a  room  from  which  we  hear  the  sounds  of  a 
violent  disturbance.  We  know  by  previous  inductions  that 
A's  disposition  is  quiet  and  peaceable;  we  know  the  same 
about  B;  and  so  we  conclude  that  C  is  responsible  for  the 
disturbance.  And  yet  we  may  be  wrong,  for  however  quiet 
and  peaceable  A  and  B  may  be  in  themselves,  there  may  be 
something  about  them — some  trait  of  disposition  or  some 
old  misunderstanding — that  makes  a  conflict  almost  inevi- 
table when  the  two  are  together. 

The  second  danger  to  which  we  are  exposed  in  using  this 
Method  of  Residues  is  that  of  overlooking  some  circumstance 
that  is  really  present,  and  of  thus  attributing  an  entirely  false 
value  to  the  presence  of  something  else.  It  may  be  that  the 
man  whose  income  we  were  inquiring  about  a  little  while 
ago  has  an  allowance  from  his  grandfather,  of  which  he  says 
nothing,  and  that  the  iron  company  is  a  source  not  of 
income  but  of  expense;  and  it  may  be  that  the  man  sus- 
pected of  peculation  is  getting  an  immense  royalty,  that  his 
employer  knows  nothing  about,  from  a  patent. 

The  third  danger  is  that  even  when  the  data  are  all  correct 
there  may  be  a  blunder  somewhere  in  our  calculations.  If 
the  bookkeeper  has  made  a  serious  mistake  in  his  addition 
or  subtraction,  all  the  reasoning  by  which  we  prove  that  a 
certain  transaction  '  must  '  have  been  responsible  for  a  gain 
or  loss  of  such  an  amount  is  worse  than  useless. 


290          METHOD   OF   CONCOMITANT   VARIATIONS. 

Of  coarse  the  way  to  make  sure  that  we  have  not  been 
misled  by  any  of  these  blunders  is  to  try  the  residual  cause 
by  itself  and  see  if  it  really  does  produce  the  precise  effect 
indicated  by  the  calculations.  Often  it  does  not,  and  where 
this  is  the  case  and  the  calculations  are  all  correct  it  indi- 
cates that  there  is  still  another  residual  cause  or  group  of 
causes  to  be  looked  for.  Often,  of  course,  direct  experiment 
is  impossible,  and  then  we  have  to  get  along  as  best  we  can 
with  the  abstract  calculations. 

In  spite  of  its  difficulties  "  the  Method  of  Residues  is  one 
of  the  most  important  among  our  instruments  of  discover)'. 
Of  all  the  methods  of  investigating  laws  of  nature,  this  is  the 
most  fertile  in  unexpected  results:  often  informing  us  of 
sequences  in  which  neither  the  cause  nor  the  effect  were 
sufficiently  conspicuous  to  attract  of  themselves  the  attention 
of  observers.  The  agent  C  [i.e.,  the  residual  cause]  may  be 
an  obscure  circumstance,  not  likely  to  have  been  perceived 
unless  sought  for,  nor  likely  to  have  been  sought  for  until 
attention  had  been  awakened  by  the  insufficiency  of  the 
obvious  causes  to  account  for  the  whole  of  the  effect.  And 
c  [the  residual  effect]  may  be  so  disguised  by  its  intermix- 
ture with  a  and  b  [the  effects  whose  causes  are  already 
known]  that  it  would  scarcely  have  presented  itself  spon- 
taneously as  a  subject  of  separate  study."  * 

The  Method  of  Residues  is,  like  all  the  rest,  a  method  of 
exhaustion;  for  we  cannot  be  sure  that  a  given  residual  effect 
is  due,  or  at  least  partly  due,  to  a  certain  residual  antecedent 
until  we  are  sure  that  that  residual  antecedent  is  the  only 
one  present  that  could  have  any  influence  on  the  effect. 

Often  it  is  impossible  to  use  any  of  the  methods  already 
discussed,  at  least  without  modification,  simply  because  it 

is  impossible  to  find  or  to  make  cases  in  which 
Method  of 

Concomitant   all    of    several   possible  causes  are   not    present. 
Variations.        '  ,  . 

suppose   that  we  want  to  know  what   makes   a 

wheel  stop  turning  after  a  while,  or  a  pendulum  stop  swine- 
*  Mill  :  Bk.  Ill,  Chap.  VIII,  Sec.  5. 


METHOD   OF   CONCOMITANT    VARIATIONS.  291 

ing,  or  a  sleigh  stop  sliding  along  a  smooth  and  level  road. 
It  may  be  the  nature  of  all  material  things  to  stop  moving 
and  come  to  rest,  or  it  may  be  the  presence  of  the  earth  that 
makes  them  do  so,  or  it  may  be  friction  or  some  resisting 
influence  exerted  by  the  air.  IIow  are  we  to  tell  ?  We 
cannot  experiment  for  the  sake  of  comparison  with  things 
that  are  not  material;  we  cannot  get  away  from  the  earth; 
we  cannot  create  conditions  in  which  there  is  absolutely  no 
friction  and  absolutely  no  air  or  other  surrounding  medium. 
We  cannot  eliminate  any  of  these  possible  causes.  How 
then  can  we  choose  between  them  ? 

Though  we  cannot  wholly  eliminate  any  of  them,  we  can 
introduce  changes  in  some  of  them,  and  if  we  find  that  the 
variation  of  any  condition  is  accompanied  by  a  variation  in  the 
result  in  question,  then  we  can  be  sure  that  that  condition 
has  some  causal  connection  with  the  result.  We  know  that 
the  presence  of  the  air  has  something  to  do  with  the  move- 
ments of  bodies,  because  we  know  that  things  stop  moving 
sooner  when  the  wind  is  against  them  than  when  there  is  no 
wind  at  all,  and  sooner  when  there  is  no  wind  at  all  than 
when  it  is  moving  with  them.  If  the  air  exerted  no  influ- 
ence, the  direction  in  which  it  moved  could  make  no 
difference  either.  This  proves  that  air  exerts  an  influence, 
at  least  when  it  moves.  That  stationary  air  also  exerts  an 
influence  and  that  this  influence  tends  to  make  a  thing  stop 
moving  can  also  be  proved;  for  a  pendulum  will  swing  or  a 
wheel  will  turn  longer  in  a  box  from  which  the  air  has  been 
partially  exhausted  than  in  one  from  which  it  has  not,  and 
the  more  nearly  the  air  is  exhausted  the  longer  the  motion 
will  continue.  So  much  for  the  influence  of  the  air;  but 
how  about  friction  ?  We  cannot  make  any  contrivance  in 
which  there  is  no  friction  at  all;  but  every  one  knows  what 
happens  when  we  diminish  it.  The  more  slippery  we  make 
a  surface  the  further  things  will  slide  upon  it,  and  the  more 
we  diminish  friction  in  wheels  and  pendulums  by  lubricants 
or  special  bearings  the  longer  they  will  keep  on  moving. 


292          METHOD   OF   CONCOMITANT   VARIATIONS. 

If  friction  did  not  affect  the  continuance  of  a  movement,  a 
vast  number  of  influences  that  agree  in  nothing  else  but  the 
diminution  of  friction  would  not  all  agree  in  prolonging  the 
movement.  Thus  we  can  use  the  Method  of  Concomitant 
Variations  to  prove  that  the  resistance  of  a  surrounding 
medium  and  friction  help  at  least  to  make  things  stop 
moving. 

To  take  another  illustration  of  the  same  method.  Suppose 
that  things  weighed  on  an  extremely  delicate  spring  balance 
seem  lighter  and  lighter,  or  that  pendulums  swing  more  and 
more  slowly,  the  farther  we  take  them  on  a  mountain  or  in 
a  balloon,  away  from  the  centre  of  the  earth,  no  matter 
which  side  of  the  earth  we  may  be  on  or  where  the  earth  may 
be  in  its  orbit.  If  the  experiments  are  tried  with  proper 
precautions,  the  distance  from  the  centre  of  the  earth  is  the 
only  condition  that  is  varied  alike  in  all  of  them,  and  the 
continual  variation  in  this  one  respect  is  invariably  accom- 
panied by  a  corresponding  variation  in  the  downward  pull 
of  everything  we  try,  whether  we  measure  that  pull  by  its 
effect  upon  the  spring  in  the  balances  or  by  its  effect  upon 
the  rate  at  which  the  pendulum  swings.  From  this  we  have 
a  right  to  conclude  that  the  nearness  of  the  earth,  and  there- 
fore the  earth  itself,  has  at  least  something  to  do  with  the 
tension  exerted  by  a  weight  upon  a  spring  and  with  the 
swinging  of  a  pendulum — and  perhaps  with  the  general 
tendency  of  things  to  fall. 

Mill's  canon  for  the  method  is  as  follows: 

"  Whatever  phenomenon  varies  in  any  manner  whenever  some 
other  phenomenon  varies  in  some  particular  manner  is  either  a 
cause  or  an  effect  of  that  phenomenon,  or  is  connected  ivith  it 
through  some  fact  of  causation." 

The  last  clause  in  the  canon  is  intended  to  cover  cases 
where  t\vo  phenomena  have  corresponding  variations,  not 
because  one  causes  the  other,  but  because  they  both  depend, 
at  least  to  some  extent,  upon  some  third  variable  which 
perhaps  has  not  been  observed  at  all.  If  we  could  be  sure 


CAUTIONS.  293 

that  there  were  only  two  variables,  we  could  be  sure  that 
one  of  them  was  the  cause,  or  at  least  a  part  of  the  cause,  of 
the  other.  Because  we  cannot  be  sure  that  one  of  the 
observed  variables  is  the  cause  of  the  other  until  we  are  sure 
that  there  is  no  third  variable  to  play  this  part  the  Method 
of  Concomitant  Variations  is  at  bottom,  like  all  the  other 
inductive  methods,  one  of  exhaustion. 

So  much  we  can  infer  according  to  the  Method  of  Con- 
comitant Variations  if  we  take  account  of  only  the  mere  fact 
of  change.  If  we  know  and  take  account  of  its  amount  also, 
we  can  often  go  further  and  find  out  with  more  or  less  cer- 
tainty how  much  the  one  variable  has  to  do  with  the  other: 
whether  it  is  the  complete  cause  or  only  a  part  of  the  cause, 
and  what  is  the  mathematical  relation  between  the  cause  and 
the  effect.  For  example,  if  we  know  that  the  income  of  a 
certain  agent  always  increases  as  his  sales  increase  and 
diminishes  as  they  diminish,  we  may  infer  from  this  that  at 
least  a  part  of  his  income  is  derived  ^from  a  commission  on 
sales;  but  that  is  all.  On  the  other  hand,  if  our  information 
is  more  definite,  and  we  know  that  when  the  sales  are 
doubled  or  quadrupled  the  income  is  also  doubled  or  quad- 
rupled, we  shall  probably  be  correct  in  inferring  that  the 
whole  income  is  derived  from  a  commission  on  sales,  and  of 
course  we  can  tell  what  the  commission  is.  If  we  know  that 
when  the  monthly  sales  amount  to  $10,000  the  income  is 
$280,  when  they  amount  to  $20,000  it  is  $480,  and  when 
they  amount  to  $40,000  it  is  $880,  we  shall  be  able  to  guess 
that  the  agent  has  a  salary  of  $80  a  month  and  a  commission 
of  two  per  cent  on  his  sales. 

In  reasoning  of  this  sort,  however,  there  are  two  things 
about  which  we  must  be  very  careful.  In  the  first  place, 

where  there  are  only  a  few  data  they  are  often 

.  ,  ,  ,    ,  ,       .        Cautions. 

consistent  with  any  one  of  several  laws  of  rela- 
tion, and  we  cannot  be  absolutely  certain  that  the  one  we 
happen  to  hit  upon  is  correct.     To  take  the  case  just  given : 
the  figures  would  be  explained  just  as  well  if  we  supposed 


294          METHOD   OF   CONCOMITANT   VARIATIONS. 

that  instead  of  receiving  any  salary  the  agent  paid  his  prin- 
cipals $120  a  month  for  his  office  or  his  '  outfit '  or  the  use 
of  their  name,  and  received  in  return  a  commission  of  four 
per  cent  on  all  sales  up  to  $10,000  a  month,  and  two  per 
cent  on  the  balance;  and  it  might  be  that  if  we  thought 
about  the  matter  long  enough  we  could  find  still  a  third 
arrangement  that  would  explain  our  data  just  as  well  as 
either  of  these. 

The  other  thing  to  be  careful  about  is  not  to  assume  that 
the  law  found  to  hold  within  certain  limits  will  necessarily 
hold  when  we  get  very  far  beyond  them.  If  we  had  enough 
more  data  which  made  it  practically  certain  in  the  case  we 
have  been  considering  that  the  agent  had  a  salary  of  $80  a 
month  and  a  commission  of  two  per  cent,  this  would  not 
prove  that  he  would  still  continue  to  get  a  salary  if  he  made 
no  sales  at  all,  nor  yet  that  he  would  continue  to  get  two 
per  cent  on  all  his  sales  if  their  number  were  very  largely 
increased.  It  might  very  well  have  been  agreed  that  on  all 
sales  over,  let  us  say,  $50,000  a  month  he  should  get  a  com- 
mission of  only  one  per  cent.  In  the  same  way,  we  may 
have  noticed  that  the  more  wind  there  is  the  more  work  it 
is  possible  to  get  out  of  a  windmill ;  but  that  is  no  reason 
for  believing  that  the  best  results  of  all  would  be  had  in  a 
hurricane,  where  the  mill  might  break  down  altogether. 
We  can  never  tell  how  far  we  are  away  from  a  point  at  which 
some  new  relation  enters  in  to  upset  all  our  calculations. 

In  spite  of  the  necessity  for  these  two  precautions,  the  fact 
that  there  are  many  cases  in  which  the  amount  of  variation 
can  be  measured  makes  this  method  particularly  useful. 
"  Although  the  most  striking  applications  of  the  Method  of 
Concomitant  Variations  takes  place  in  the  cases  in  which  the 
Method  of  Difference,  strictly  so  called,  is  impossible,  its  use 
is  not  confined  to  those  cases;  it  may  often  usefully  follow 
after  the  Method  of  Difference,  to  give  additional  precision 
to  a  solution  which  that  has  found.  When  by  the  Method 
of  Difference  it  has  first  been  ascertained  that  a  certain 


CAUTIONS.  295 

object  produces  a  certain  effect,  the  Method  of  Concomitant 
Variations  may  be  usefully  called  in,  to  determine  according 
to  what  law  the  quantity  or  the  different  relations  of  the 
effect  follow  those  of  the  cause."  * 

When  the  Method  of  Concomitant  Variations  is  used  in 
this  way  to  give  precision  to  causal  laws,  it  is  obvious  that 
it  rests  no  longer  upon  the  bare  assumption  that  every  event 
has  a  cause,  but  upon  the  more  refined  assumption  that  the 
amount  of  the  cause  is  related  to  the  amount  of  the  effect  by 
some  law  of  definite  proportion. 

*  Mill :    Bk.  Ill,  Chap.  VIII,  Sec.  6. 


CHAPTER   XXX. 
GROUP   COMPARISONS,  OR   THE   METHOD   OF  STATISTICS. 

IN  the  examples  already  given,  the  Method  of  Concomitant 
Variations  was  applied  in  the  following  way.  We  noticed 
the  state  or  action  of  some  individual  thing,  then  introduced 
a  change  into  the  surroundings  and  noticed  what  change 
followed  in  the  state  or  action  of  the  same  individual.  We 
compared  the  time  which  it  takes  for  a  pendulum  principie 
to  make  a  complete  oscillation  (or  a  hundred  anduses- 
continuous  oscillations)  when  it  is  swung  at  the  level  of  the 
sea  and  when  it  is  swung  at  various  distances  above  it,  or 
we  compared  the  distance  that  a  spring  is  stretched  or 
twisted  by  some  heavy  object  attached  to  it  at  the  level  of 
the  sea  and  at  various  distances  above  it.  In  all  the  experi- 
ments necessary  for  such  comparisons  we  swung  the  same 
pendulum  or  weighed  against  our  spring  the  same  lump  of 
lead.  This,  however,  was  not  absolutely  necessary.  If  we 
were  quite  certain  that  two  pendulums  or  two  lumps  of  lead 
were  exactly  alike  in  every  essential  respect,  we  could  use  one 
at  the  level  of  the  sea  and  the  other  at  the  mountain-top, 
and  still  draw  our  conclusion  from  the  difference  in  the 
results.  But  whether  the  individuals  compared  were  identi- 
cal or  not,  in  either  case  we  compared  the  states  or  actions 
of  single  individuals.  Moreover  it  will  be  remembered  that 
to  draw  any  conclusion  from  the  results  of  such  a  compari- 
son we  had  to  be  sure  that  the  change  in  elevation  was  the 
only  change  made  that  might  affect  the  downward  pull  in 

2q6 


PRINCIPLE   AND   USES.  297 

question.  If  that  downward  pull  had  been  subject  to  varia- 
tion from  a  hundred  other  causes  known  and  unknown, 
whose  influence  we  could  not  possibly  estimate,  then  the 
experiment  could  have  told  us  nothing  about  the  effect  upon 
that  pull  of  the  changed  distance  from  the  centre  of  the 
earth. 

In  cases  of  this  latter  sort  inferences  that  cannot  be  based 
upon  what  happens  in  the  case  of  a  single  individual  can  be 
based  upon  the  total  or  average  change  produced  in  a  very 
large  number.  We  know,  for  example,  that  the  growth  of 
a  child  as  measured  by  its  weight  depends  not  only  upon  its 
age,  but  also  upon  a  vast  number  of  other  influences:  its 
own  natural  vitality,  the  size  of  its  parents,  the  nature  and 
amount  of  its  food,  the  amount  of  sunlight  and  fresh  air  to 
which  it  is  exposed,  its  freedom  from  disease,  its  exercise, 
its  happiness,  and  so  on;  and  we  cannot  possibly  tell  how 
much  influence  any  one  of  these  has  exerted  upon  the  growth 
of  an  individual  child.  Consequently  we  can  tell  very  little 
about  the  growth  due  to  age  by  weighing  a  child  when  it  is 
six  and  again  when  it  is  seven;  much  less  by  comparing  the 
weight  of  one  child  of  six  with  that  of  another  child  of  seven. 
Yet  if  we  compare  the  average  weight  of  several  thousand 
children  of  six  with  that  of  several  thousand  children  of  seven 
selected  in  the  same  way  from  the  same  neighborhood,  then 
we  shall  have  a  right  to  infer  that  the  difference  in  the 
average  weights  is  due,  to  a  fraction  of  one  per  cent,  to  the 
difference  in  age.  If  one  child  of  seven  has  attained  its 
growth  under  better  conditions  than  some  child  of  six,  there 
is  undoubtedly  some  child  of  six  that  has  attained  its  growth 
under  better  conditions  than  some  child  of  seven;  so  that  on 
the  whole  the  favorable  and  the  unfavorable  influences  in  the 
two  groups  are  balanced  evenly  enough  to  be  disregarded. 
Thus  by  comparing  large  enough  groups  we  can  often 
eliminate  the  effects  of  all  the  causes  but  those  under  con- 
sideration and  get  a  very  accurate  measure  of  the  effect 
exerted  by  the  latter. 


298  GROUP   COMPARISONS. 

This  Method  of  Group  Comparison  is  used  very  commonly 
at  the  present  time,  especially  in  physiology,  psychology,  and 
economics,  to  estimate  the  effect  of  various  influences  that 
cannot  possibly  be  isolated  from  a  great  many  others,  and 
whose  results  cannot  be  estimated  with  accuracy  in  any  other 
way.  To  take  a  practical  example. 

Is  there  any  connection  between  a  child's  size,  as  distin- 
guished from  its  age,  and  its  mental  development  ?  We 
should  be  able  to  answer  this  question  if  we  can  find  out 
whether  large  children  are  better  developed  mentally  than 
smaller  children  of  the  same  age,  or,  what  amounts  to  the 
same  thing,  whether  children  of  better  mental  development 
are  larger  on  the  whole  than  children  of  the  same  age  of 
poorer  mental  development.  To  find  this  out  an  investi- 
gator takes  through  the  teachers  of  a  large  city  the  ages  and 
weights  of  some  thirty  thousand  pupils  in  the  public  schools. 
He  then  finds  the  average  weight  of  all  the  pupils  of  the 
same  sex  and  age  throughout  the  schools,  as  well  as  the 
average  weight  of  all  the  pupils  of  the  same  sex  and  age  in 
each  '  grade  '.  Comparing  these  averages  together  he  finds 
that  in  practically  every  case  children  in  higher  grades  weigh 
more  than  children  of  the  same  age  and  sex  in  lower  grades. 
Accepting  the  progress  which  a  child  makes  in  school  as  a 
fair  enough  test  of  its  mental  development,  and  the  grade  in 
which  it  is  found  as  a  fair  enough  test  of  its  progress,  he 
concludes  from  this  that  children  with  greater  mental 
development  are  on  the  whole  larger  than  children  of  the 
same  age  with  less  mental  development.*  From  such  a 
conclusion,  rightly  established,  we  should  have  a  right  to 
infer  that  a  child's  mental  development  depends  not  merely 
upon  its  age,  but  upon  the  development  of  its  body,  or, 
conversely,  that  the  development  of  the  body  depends  not 
merely  upon  age,  but  upon  the  development  of  the  mind, 
or  else  that  the  development  of  the  mind  and  the  develop- 

*  Sec  Transactions  of  the  Academy  of  Science  of  St.  Louis,   Vol.  VI, 
No.  7. 


PRINCIPLE   AND   USES.  299 

ment  of  the  body  both  depend  largely  upon  the  same  con- 
ditions; in  short,  that  there  is  a  close  causal  relation  between 
them. 

Here  is  an  example  of  the  measurements: 

Average  weight  of         2188  boys  nine  years  old    57.41  Ibs. 
"  "        "  the    570  of  these  in  Grade  I    55.52     " 

„    ,.    II95  .,      ..      ,.       ..     ii    57.56     „ 

357 '   "  HI  59-26  " 

„          ..      .,    ,.      44  ..     •,     ..      ..   IV   Gl.QI    ii 

Twenty-two  boys  out  of  the  total  of  2188  who  were  meas- 
ured are  not  accounted  for  in  this  table.  These  twenty- 
two  boys  must  have  been  in  the  Kindergarten  and  the  grades 
higher  than  the  fourth.  Their  measurements  are  not  aver- 
aged because  the  investigator  thought,  very  properly,  that  an 
average  could  not  be  depended  upon  unless  it  were  based 
upon  at  least  twenty  individual  measurements. 

The  table  shows  a  difference  in  weight  of  about  two 
pounds  between  boys  of  nine  in  one  grade  and  those  in  the 
grade  above  it;  so  that  between  the  boys  of  nine  in  the  first 
grade  and  those  in  the  fourth  there  is  the  very  decided  differ- 
ence in  the  average  of  over  six  pounds.  The  very  consider- 
able size  of  these  differences,  the  almost  unbroken  regularity 
with  which  they  appear  from  one  grade  to  the  next,  not  only 
with  boys  of  nine,  but  with  both  boys  and  girls  of  all  ages 
between  six  and  sixteen  or  seventeen,  and  the  large  number 
of  total  measurements,  to  say  nothing  of  certain  other  rela- 
tions brought  out  in  the  original  article, — all  these  prove 
that  the  different  average  weights  in  different  grades  cannot 
be  the  result  of  mere  chance — that  there  must  be  some  real 
cause  at  work  which  tends  to  make  the  boys  or  girls  of  a 
given  age  in  a  higher  class  heavier  than  those  in  a  lower 
class.  In  this  way,  by  comparing  the  average  measurements 
of  several  large  groups  we  can  often  prove  the  existence  of 
causal  relations  which  we  could  never  prove  by  merely  com- 
paring a  few  individuals. 


300  GROUP   COMPARISONS. 

The  errors  to  which  we  are  liable  in  such  investigations  as 
this  are  very  serious.  In  the  first  place  we  must  make  sure 
number  of  t^at  enough  measurements  are  made  to  eliminate 
data.  the  effects  of  purely  individual  idiosyncrasies. 

One  boy  with  twenty  pounds  of  extra  fat  would  make  a 
difference  of  two  pounds  in  the  average  when  he  is  one  of 
only  ten;  but  he  makes  a  difference  of  only  one  fiftieth  of  a 
pound  when  he  is  one  of  a  thousand.  In  general,  the  larger 
the  groups  from  which  we  get  our  averages,  the  less  chance 
there  is  that  the  distribution  of  peculiar  individuals  will  be 
uneven  enough  to  make  a  difference  worth  considering  in  the 
results.  In  the  table  it  will  be  noticed  that  the  difference 
between  nine-year-old  boys  in  the  third  grade  and  those  in 
the  fourth  is  slightly  greater  than  that  between  any  other 
two  successive  grades.  This  extra  difference  might  well  dis- 
appear if  instead  of  forty-four  boys  in  the  fourth  grade  to 
examine  there  had  been  a  thousand.  The  accuracy  with 
which  we  should  read  our  averages  always  depends  upon  the 
number  of  measurements  from  which  the  average  is  com- 
puted. 

A  second  blunder  to  be  avoided  in  statistical  investigations 
where  the  data  are  supplied  by  different  observers  arises  from 

what  is  called  the  '  Personal  Equation  '  of  the 
Personal 

equation,  observers.  \\  here  there  is  any  doubt  about  a 
etc. 

quantity  some  people  constantly  tend  to  over- 
estimate it,  others  to  underestimate  it.  If  one  object  or 
set  of  objects  happens  to  be  measured  by  a  person  who 
habitually  overestimates,  and  another  by  one  who  habitually 
underestimates,  it  is  evident  that  the  difference  between  the 
two  will  appear  a  little  larger  or  a  little  smaller  than  it 
really  is.  Personal  equation  of  this  general  sort  appears  in 
many  different  forms.  If  each  of  two  people  has  to  press  a 
button  the  moment  he  sees  a  certain  sight  or  hears  a  cer- 
tain sound,  the  chances  are  that  they  will  not  both  press  it 
at  exactly  the  same  time.  One  will  nearly  always  act  a 
fraction  of  a  second  later  than  the  other.  The  more  prac- 


PERSONAL   EQUATION,   ETC.  301 

tice  each  of  the  two  has  had  in  this  sort  of  reaction  the  more 
likely  he  is,  not  to  be  more  accurate,  but  to  be  more  con- 
stant in  his  error;  and  therefore  the  more  likely  it  is  that 
the  interval  between  the  reactions  of  the  two  observers  or 
experimenters  will  always  be  about  the  same,  so  that  proper 
allowance  can  be  made  for  it.  In  this  way  two  astrono- 
mers may  always  differ  by  perhaps  a  tenth  of  a  second  of 
time  in  the  records  which  they  make  of  the  movements  of 
the  heavenly  bodies;  and  before  they  come  to  put  their 
results  together  they  always  find  out  what  the  personal  equa- 
tion of  each  observer  is  and  make  due  allowance  for  it. 
Another  example  of  this  general  kind  of  personal  equation 
is  found  in  our  different  estimates  of  distance.  In  trying  to 
find  the  centre  of  a  horizontal  line,  some  people  habitually 
go  too  far  to  the  right,  others  too  far  to  the  left;  and  when 
we  are  asked  to  estimate  the  relative  lengths  of  a  horizontal 
line  and  a  vertical  line  which  is  actually  precisely  equal 
to  it,  almost  everybody  will  say  that  the  vertical  line  seems 
a  little  longer,  but  the  error  will  be  greater  with  some  people 
than  with  others. 

There  is  a  similar  difference  between  people  in  the  use  of 
words  whose  meaning  is  rather  vague.  If  we  are  comparing 
the  amount  of  drunkenness  in  different  cities,  we  must  be  sure 
that  the  persons  who  collected  the  statistics  all  defined  the 
term  in  the  same  way.  It  may  be  that  in  one  city  a  man 
was  called  drunk  when  he  had  imbibed  enough  alcohol  to 
make  him  noisy,  in  a  second  when  he  staggered,  and  in  a 
tlr'rd  not  until  he  fell  down.  The  terms  '  sick  ',  '  typhoid 
fever  ',  '  pauper  ',  '  criminal  ',  '  morbid  ',  and  a  host  of  others 
are  subject  to  variations  of  this  sort  in  their  definition. 

In  comparing  the  official  statistics  of  different  places  or 
periods  we  must  be  careful  to  see  not  only  that  the  terms  are 
defined  in  the  same  way  in  them  all,  but  also  to  see  that 
about  the  same  proportion  of  actual  cases  are  reported.  In 
some  places  a  much  larger  per  cent  of  the  actual  births, 
contagious  diseases,  or  crimes  is  reported  than  in  others. 


302  GROUP  COMPARISONS. 

Much  the  easiest  way  for  a  police  department  to  diminish 
disorderliness — on  paper — is  to  instruct  the  patrolmen  to 
report  as  few  cases  as  possible. 

Another  source  of  error,  very  much  like  personal  equation, 
is  due  to  preconceived  opinions  on  the  part  of  the  observers 
as  to  what  the  result  of  the  investigation  should 
tionsand  be.  This  danger  is  especially  likely  to  affect 
statistical  inquiries  that  depend  upon  data  fur- 
nished by  a  set  of  observers  untrained  in  that  kind  of  work. 
But  it  is  hard  enough  for  any  one  to  avoid,  even  in  taking 
what  we  call  exact  measurements.  No  measurements  are 
absolutely  accurate;  and  if  it  is  a  question  of  whether  some- 
thing measures  26.2  units  or  26.3  our  decision  is  likely  to  be 
influenced  more  than  we  realize  by  the  desire  to  give  our 
theory  the  benefit  of  the  doubt.  Hence  it  is  advisable  to 
take  each  measurement  in  such  a  way  that  it  is  impossible 
to  tell  which  side  of  the  question  it  will  help  until  it  is  not 
only  taken  but  recorded;  and  after  we  do  know  its  bearing 
it  should  not  be  subject  to  revision.  When  the  measure- 
ments are  taken  by  assistants  untrained  in  such  work  it  is 
wise  to  begin  with  a  small  preliminary  investigation  in  order 
to  make  sure  that  the  instructions  are  absolutely  full  and 
clear,  and  in  many  cases  it  is  also  desirable  to  exclude  any 
possible  influence  of  prejudice  by  leaving  the  assistants  in 
complete  ignorance  as  to  the  question  at  issue,  though  this 
should  not  be  done  if  they  will  imagine  that  the  issue  is 
something  else  in  which  they  are  more  interested. 

This  effect  of  prejudice  upon  our  measurements  is  not 
confined  of  course  to  group  comparisons.  It  is  found  every- 
where. Every  teacher  knows  how  much  easier  it  is  to  grade 
an  examination  paper  fairly  when  he  does  not  know  who 
wrote  it  than  when  lie  does.  A  phrase  used  by  a  good 
student  may  suggest  all  that  he  probably  knows  and  thus 
get  a  high  mark,  while  the  very  same  phrase  from  a  poor  one 
suggests  all  his  stupidities  and  gets  a  low  mark.  Hence  the 
teacher  who  really  means  to  be  guided  in  making  his  grades 


PRECONCEPTIONS   AND   INTERESTS.  303 

by  the  face  of  the  returns  will  try  to  read  and  mark  the 
papers  before  he  knows  whose  they  are,  and  even  to  mark 
the  answer  to  each  separate  question  before  he  knows  pre- 
cisely what  effect  that  particular  mark  will  have  upon  the 
unknown  student's  standing  as  a  whole,  e.g.,  whether  it  is 
or  is  not  barely  enough  to  pass  him  or  to  give  him  honors. 
The  less  strongly  we  feel  the  issues  at  stake  the  more 
accurately  we  are  likely  to  judge. 

The  effect  of  preconceptions  and  personal  interests  appears 
again  in  the  selection  of  cases.  If  a  teacher  wishes  to  show 
how  bad  his  class  is,  he  will  put  more  doubtful  cases  in  his 
list  of  those  who  are  disorderly  or  deficient  than  if  he  wishes 
to  show  how  good  it  is.  So  with  purely  theoretical  ques- 
tions. To  go  back  to  our  old  example.  Suppose  the  ques- 
tion to  be  settled  by  weighing  the  children  in  the  various 
grades  had  been  hotly  discussed  by  the  teachers  who 
afterwards  took  the  weights.  How  natural  it  would  be  for 
some  of  them,  unless  they  had  most  explicit  instructions  to 
the  contrary,  to  omit  the  weight  of  this  or  that  individual 
pupil  on  the  ground  that  to  include  it  in  the  set  from  which 
an  average  is  made  would  be  manifestly  unfair!  '  Johnny  is 
very  bright  and  very  small;  but  then  he  is  a  cripple,  and  it 
is  certainly  not  fair  to  include  him  ';  '  Mary  is  a  great  big 
girl  in  the  second  grade,  but  they  really  should  have  let  her 
into  the  third,  so  I  will  not  include  her '.  If  we  begin  in 
this  way  to  include  only  the  cases  that  seem  to  us  reasonable, 
it  is  perfectly  evident  that  our  views  of  what  is  reasonable  in 
any  particular  case  will  depend  very  largely  upon  what  we 
think  beforehand  about  the  question  at  issue;  and  as  the 
result  of  the  whole  investigation  will  be  influenced  by  our 
decision  in  these  particular  cases,  there  is  always  a  strong 
tendency  for  the  investigation  to  merely  confirm  the  opinion 
we  had  to  begin  with.  For  this  reason  it  is  always  desirable 
to  lay  down  rules  of  procedure  beforehand  that  leave  no 
room  whatever  for  selective  judgment  during  the  course  of 
the  investigation.  Undoubtedly  it  often  is  unfair  in  making 


304  GROUP   COMPARISONS. 

up  an  average  to  include  exceptional  cases.  But  the  only 
safe  way  to  overcome  the  unfairness  is  to  base  the  average 
on  so  many  cases  that  it  will  make  practically  no  difference 
in  that  average  whether  a  few  exceptions  are  included  or  not. 
If  any  such  large  number  of  cases  is  not  available,  then  the 
statistical  method  is  not  reliable.  We  appeal  to  statistics 
because  we  wish  impartial  witnesses  instead  of  mere  in- 
dividual opinions,  and  it  is  obviously  absurd  to  run  the 
slightest  chance  of  selecting  some  of  the  witnesses  because 
they  will  testify  in  our  favor  and  excluding  others  because 
they  will  testify  against  us. 

However  successful  we  may  be  in  avoiding  the  influence 
of  our  own  personal  equation  or  that  of  others  in  the  selec- 
Accidental  t'on  an^  measurement  of  cases,  we  may  still 
selection.  choose  our  cases  according  to  some  plan  that 
does  involve  an  unfair  selection  though  we  do  not  realize  it. 
The  method  of  group  comparisons  is  based  on  the  assump- 
tion that  the  force  under  investigation  is  the  only  one  which 
does  not  act  about  as  much  upon  the  members  of  one  of  the 
groups  compared  as  upon  the  members  of  the  other.  But 
if  this  assumption  is  not  correct,  if  some  other  force  is  present 
which  really  does  act  more  upon  the  members  of  one  group 
than  upon  the  members  of  the  other,  and  if  we  overlook  its 
presence,  it  is  clear  enough  that  we  shall  attribute  too 
much  or  too  little  to  the  force  we  are  investigating;  we  sup- 
posed we  had  excluded  all  other  constant  causes,  and  we  had 
not. 

Suppose,  for  example,  whether  it  be  true  or  not,  that  the 
further  a  child  gets  in  school  the  better  able  he  is  either  to 
help  his  parents  at  home  or  to  earn  money  for  them  outside. 
It  is  evident  that  the  poorest  and  most  shiftless  parents  will 
be  tempted  to  take  their  children  out  of  school  as  soon  as 
their  labor  is  worth  a  very  few  cents  a  day;  and  unless  the 
law  is  enforced  very  rigorously  they  will  find  means  of  doing 
so.  Others  less  poor  or  less  improvident  will  allow  their 
children  to  go  a  little  farther.  This  process  would  continue 


ACCIDENTAL   SELECTION.  305 

from  grade  to  grade,  until  in  the  high  school  nearly  all  the 
children  represented  homes  that  are  fairly  comfortable  and 
well-ordered.  It  is  evident  that  causes  of  this  sort  would 
produce  a  process  of  partial  selection  on  some  basis  other 
than  that  of  the  children's  individual  mental  development. 
Many  of  the  children  in  the  lowest  grades  would  be  paupers; 
those  in  the  highest  would  not.  In  such  a  case  it  might 
well  be  that  the  difference  in  weight  between  children  of  the 
same  age  in  lower  and  in  higher  grades  is  due,  at  least  in 
part,  to  the  fact  that  the  latter  come  on  the  whole  from  more 
prosperous  families,  and  are  therefore  better  fed  and  cared  for. 

If  it  should  turn  out  upon  investigation  that  there  is 
nothing  in  this  suggestion,  we  might  offer  another  somewhat 
different.  Suppose  that  amongst  the  most  ignorant  classes, 
in  a  city  there  is  for  some  reason  or  other  a  rather  hostile 
feeling  towards  the  public  schools,  so  that  the  most  ignorant 
parents  keep  their  children  out  of  them  as  long  as  they 
possibly  can;  while  parents  of  the  better  classes,  on  the 
other  hand,  send  them  just  as  soon  as  they  can.  This  would 
of  itself  tend  to  put  children  from  the  better  homes  in  higher 
grades  than  those  of  the  same  age  from  the  worse  homes. 
Moreover,  in  the  better  homes  children  are  helped  with  their 
lessons  and  encouraged  to  keep  up  with  their  class,  or  ahead 
of  it,  while  in  the  worse  they  are  not.  In  this  way  children 
who  are  better  cared  for  at  home,  and  therefore  probably 
larger,  would  tend,  apart  altogether  from  any  mental 
superiority  of  their  own,  to  be  farther  along  in  school  than 
those  who  are  less  well  cared  for  at  home.  But  there  is  still 
another,  more  direct,  consideration  in  the  case  we  have  sup- 
posed. The  smaller  the  child  the  longer  can  a  parent 
prejudiced  against  the  schools  pass  him  off  as  too  young  to 
be  sent;  and  the  larger  the  child  the  easier  it  is  for  the 
intelligent  parent  who  wants  him  to  go  to  school  to  persuade 
the  authorities  that  he  is  really  mature  enough  to  begin,  even 
if  he  is  not  quite  up  to  the  legal  age. 

If  it  is  customary  in  the  city  in  question  to  promote  nearly 


306  GROUP  COMPARISONS. 

all  the  children  at  the  end  of  the  year  whether  they  have 
accomplished  very  much  during  the  year  or  not,  it  is  evident 
that  a  child's  grade  in  the  schools  of  such  a  city  would 
depend  far  less  upon  his  mental  development  than  upon  the 
age  at  which  his  school  career  happened  to  begin.  Thus 
there  might  be  a  double  or  triple  reason  why  large  children 
should  be  farther  along  in  school  than  small  ones,  apart 
altogether  from  any  difference  in  their  own  mental  develop- 
ment. 

When  such  objections  as  these  are  offered  to  the  conclu- 
sions which  any  one  draws  from  a  set  of  statistics,  the  way  to 
answer  them  is  to  find  out  by  supplementary  inquiries 
whether  the  causes  suggested  really  are  at  work  in  the  case 
in  question;  and  if  they  are,  to  estimate  the  amount  of  effect 
which  they  are  likely  to  produce,  and  thus  see  how  much  of 
the  total  effect  is  left  for  the  causes  originally  assigned.  Until 
conclusions  based  upon  the  method  of  group  comparison  have 
been  subjected  to  much  critical  examination  of  this  sort,  we 
must  not  attach  to  them  anything  like  absolute  confidence. 

Another  danger  which  confronts  this  method  of  group 
comparisons — and  indeed  all  methods  that  depend  upon 
Misplaced  precise  measurements — is  that  we  shall  infer  the 
accuracy.  presence  of  some  cause  from  numerical  computa- 
tions that  are  far  too  precise  for  the  data  from  which  they  are 
derived.  By  this  I  mean  too  precise  for  the  least  accurate  of 
the  data.  When  mathematicians  take  two  sets  of  measure- 
ments which  are  to  enter  into  the  same  problem,  and  when 
they  can  only  get  a  certain  proportion  of  accuracy  in  one, 
they  realize  that  the  inaccuracy  of  these  data  will  affect  the 
problem  as  a  whole  in  the  same  proportion,  and  so  they  make 
no  effort  to  get  a  greater  degree  of  accuracy  in  any  of  the 
other  data.  For  example,  suppose  we  know  that  one  side, 
B,  of  a  triangle  is  twelve  times  as  long  as  the  base,  A,  and 
that  we  measure  A  for  the  sake  of  finding  the  length  of  B. 
If  A  is  really  101  inches  long  but  we  make  it  100  inches, 
that  will  mean  that  B  is  really  101  feet  long,  though  we  cal- 


MISPLACED   ACCURACY.  307 

culate  that  it  is  just  roo  feet.  In  this  way,  an  error  of  one 
inch  in  the  length  of  A  corresponds  to  an  error  of  twelve 
inches  in  the  length  of  B.  If  we  measured  both  A  and  B  for 
the  sake  of  comparing  them  and  did  not  try  to  measure  A 
more  accurately  than  in  even  inches,  it  would  be  a  waste  of 
time  to  measure  B  more  accurately  than  in  even  feet. 
Moreover,  it  would  be  a  positive  blunder  to  say  that  A 
measured  'exactly'  100  inches;  that  B  measured  'exactly' 
100  feet  and  i  inch;  and  that  B  was  therefore  a  little  more 
than  twelve  times  as  long  as  A.  If  we  measure  B  to  an  inch, 
we  must  measure  A  to  a  twelfth  of  an  inch  before  we  insti- 
tute any  such  precise  comparisons  between  them,  or  draw 
any  conclusion  from  the  existence  of  such  slight  discrepan- 
cies. When  we  multiply  a  measurement  \ve  multiply  the 
error  that  we  made  in  taking  it;  when  we  divide  a  measure- 
ment we  divide  the  error.  So  in  general  we  can  say  that 
any  figure  which  has  to  be  multiplied  before  it  is  added  to, 
or  subtracted  from,  or  compared  in  any  way  with,  another 
should  be  reached  by  more  careful  measurements  than  that 
other;  while  a  figure  which  has  to  be  divided  before  it  is 
compared  with  another  may  be  reached  by  less  careful 
measurements  than  that  other. 

To  take  another  example  of  this  law  of  proportion  in  the 
accuracy  with  which  we  should  take  various  measurements. 
A  certain  horse  trots  a  mile  in  about  two  minutes  and  five 
seconds.  The  stop-watches  by  which  he  is  timed  will 
register  fifths  of  a  second,  but  nothing  less.  If  we  wish  to 
find  his  speed  as  accurately  as  possible,  how  accurately 
should  we  measure  the  course  over  which  he  trots  ?  A  horse 
trotting  at  the  rate  given  goes  more  than  eight  feet  in  a  fifth 
of  a  second,  and  since  the  watches  will  not  register  any  time 
less  than  a  fifth  of  a  second,  they  are  absolutely  incapable  of 
measuring  the  time  that  it  takes  the  horse  to  go  eight  feet  or 
less.  It  would  therefore  be  a  waste  of  time  to  measure  the 
course  for  such  a  horse  to  a  fraction  of  an  inch.* 

*  Absurd,  I  mean,  if  we  are  measuring  the  track  merely  for  the  sake 


308  GROUP  COMPARISONS. 

Indeed,  the  very  precision  of  such  measurement  might  be 
misleading.  Suppose,  for  example,  that  horse  A  trots  over 
the  mile  track  in  New  York  in  two  minutes  and  five  and  one- 
fifth  seconds,  and  that  horse  B  trots  over  the  mile  track  in 
Toronto  in  the  same  time.  Suppose  also  that  accurate 
measurements  show  the  Toronto  track  to  be  really  six  feet 
longer  than  the  New  York  track.  How  natural  it  would  be 
to  say  that  since  B  went  six  feet  farther  than  A  in  the  same 
time,  he  must  have  gone  faster!  But  this  conclusion  is  abso- 
lutely unwarrantable;  for  when  we  say  that  the  two  distances 
were  covered  in  '  the  same  time  '  we  mean  that  in  each  case 
the  time  was  at  least  as  much  as  2.5!  and  less  than  2_5|. 
In  other  words,  we  mean  that  the  difference  between  the  two 
was  less  than  a  fifth  of  a  second.  But  with  a  possible  differ- 
ence in  the  time  of  almost  a  fifth  of  a  second  it  may  be  that 
A  really  trotted  faster  than  B  after  all.* 

In  our  example  of  group  comparisons  I  think  we  find  a 
blunder  of  this  same  sort.  The  other  objections  which  we 
made  to  the  conclusion  based  upon  the  weights  of  school 
children  in  different  grades  were  largely  hypothetical.  This 
objection  is  real.  The  investigator's  object  is  to  find  out 
what  difference  there  is  in  the  weights  of  pupils  of  the  same 
age  who  are  in  different  grades.  In  the  tables  which  he  gives 
for  comparison  the  average  weights  are  all  calculated  to  the 
hundredth  part  of  a  pound.  How  accurate  should  he  have 
been  in  finding  the  average  ages  ?  If  we  take  account  of  a 
difference  in  weight  of  one  pound,  should  we  not  take 
account  of  a  difference  in  age  that  is  sufficient  to  produce 

of  timing  that  particular  horse  with  that  particular  kind  of  watch.  The 
accuracy  is  justified  by  the  fact  that  some  time  we  may  have  a  better 
watch  or  wish  to  time  a  slower  animal. 

*  It  is  assumed  for  the  sake  of  simplicity  in  the  argument  that  the 
stop-watch  really  will  measure  with  accuracy  to  the  fifth  of  a  second. 
When  we  remember  that  the  starting  and  stopping  of  the  watch  depend 
upon  human  action  in  the  midst  of  exciting  surroundings,  it  is  evident 
enough  that  there  is  still  less  accuracy  in  the  measurement  of  the  horse's 
time. 


MISPLACED   ACCURACY.  309 

that  difference  of  one  pound  ?  If  we  take  account  of  a 
difference  in  weight  of  one  hundredth  of  a  pound,  should 
we  not  take  account  of  a  difference  in  age  sufficient  to  pro- 
duce that  difference  of  one  hundredth  of  a  pound  ?  IIo\v 
much  is  this  ? 

According  to  the  tables  the  average  weight  of  all  the  boys 
examined  who  are  eight  at  their  nearest  birthday  is  52  39 
pounds;  the  average  weight  of  all  the  boys  who  are  nine  at 
their  nearest  birthday  is  57.41  pounds;  and  the  average 
weight  of  all  the  boys  who  are  ten  at  their  nearest  birthday 
is  62.38  pounds.  This  means  that  the  boys  gain  about  live 
pounds  a  year,  or  about  a  tenth  of  a  pound  a  week,  and  the 
hundredth  part  of  a  pound  in  less  than  a  day.* 

This  law  of  average  growth  means  that  we  cannot  draw 
any  conclusion  from  an  average  difference  in  weight  of  one- 
tenth  of  a  pound  between  two  groups  of  children  'of  the 
same  age  ',  unless  we  have  good  reason  to  believe  that  the 
age  really  is  '  the  same  '  not  merely  to  a  year  but  to  a  week. 
A  difference  of  a  week  in  age  would  account  for  a  difference 
of  a  tenth  of  a  pound  in  weight.  In  the  same  way  a  differ- 
ence of  ten  weeks  in  age  would  account  for  a  difference  of  a 
pound  in  weight,  and  a  difference  of  twenty  weeks  for  the 
difference  of  two  pounds  which  the  tables  show  between  the 
boys  of  nine  in  any  two  successive  grades. 

And  now  the  question  comes:  Have  we  a  right  to  believe 
that  there  is  no  such  difference  as  this  in  the  ages  ? 

In  the  tables  before  us  the  children  are  grouped  according 
to  their  age  in  years  at  their  nearest  birthday.  Xo  account 
is  taken  of  months  or  days.  In  each  group,  then,  there  will 
be  some  children  who  are  almost  a  year  older  than  some 
others  in  the  same  group.  But  since  it  is  fair  to  assume  that 
there  are  about  as  many  children  a  little  under  a  given  age 

*  We  assume  here  for  the  sake  of  simplicity  that  the  growth  is  uni- 
form throughout  the  year.  If  we  took  account  of  the  fac^  that  it  is  not 
it  would  complicate  the  argument,  but  it  would  not  affect  the  principle 
on  which  it  is  based. 


310  GROUP   COMPARISONS. 

as  a  little  over  it,  the  average  age  of  all  the  children  called 
nine  would  really  be  almost  exactly  nine;  and  so  with  each 
of  the  other  ages.  In  this  way  we  have  a  right  to  assume 
that  the  difference  in  average  weight  between  all  the  boys 
called  nine  and  all  the  boys  called  ten  corresponds  to  a  very 
definite  difference  in  age  of  almost  precisely  one  year.  Thus 
this  inference  based  upon  the  tables  is  perfectly  correct,  and 
we  have  a  right  to  say  that  it  really  is  a  difference  of  one 
year  in  age  which  makes  the  difference  of  about  five  pounds 
in  weight. 

This,  however,  is  very  different  from  saying  that  the  boys 
called  ten  in  any  one  grade  are  on  the  average  a  year  older 
than  the  boys  called  nine  in  the  same  grade,  or  that  the 
boys  called  nine  in  one  grade  are  on  the  average  precisely 
as  old  as  the  boys  called  nine  in  another. 

In  fact  the  presumption  is  all  the  other  way.  A  boy 
exactly  eight  years  and  six  months  of  age  is  quite  as  likely 
to  be  in  a  grade  with  the  boys  of  eight  at  their  nearest  birth- 
day as  with  the  boys  of  nine;  and  a  boy  of  eight  years  and 
seven  months  is  almost  as  likely  to  be.  On  the  other  hand 
a  boy  of  nine  years  and  six  months  is  quite  as  likely  to  be 
with  the  boys  of  ten  as  with  the  boys  of  nine,  and  a  boy  of 
nine  years  and  five  months  is  almost  as  likely  to  be.  In  this 
way  one  boy  of  nine  might  easily  be  two  grades  ahead  of 
another,  not  because  he  is  any  better  developed  for  his  age, 
but  merely  because  he  is  ten  or  eleven  months  older.  And 
thus,  in  general,  there  is  every  reason  to  believe  that  the  boys 
of  a  given  age  in  a  higher  grade  are  considerably  older  on  the 
average  than  those  '  of  the  same  age  '  in  a  lower  grade;  and 
the  difference  in  age  might  well  account  for  a  large  part  of 
the  difference  in  weight.  It  could  not  account  for  a  differ- 
ence of  five  pounds,  of  course;  for  the  difference  in  age  must 
always  be  less  than  a  year.  Hence  it  could  not  account  for 
all  the  difference  which  is  found  between  boys  of  nine  in  the 
first  grade  and  those  in  the  fourth;  but  it  might  account  for 
enough  of  it  to  make  the  conclusion  that  bright  children  are 


MISPLACED   ACCURACY.  311 

larger  than  dull  ones  extremely  doubtful.  Precisely  how 
much  the  actual  difference  in  age  really  will  account  for  we 
cannot  tell  until  the  age  of  each  child  is  taken  accurately 
enough  to  show  precisely  what  this  difference  is. 

There  is  a  difference  between  this  example  of  conclusions 
too  precise  for  the  data  upon  which  they  are  based  and  the 
one  given  before  it.  When  we  compared  two  individuals 
and  concluded  that  the  horse  B  was  faster  than  the  horse  A 
because  it  trotted  a  few  feet  farther  '  in  the  same  time  ',  our 
conclusion  may  have  been  wrong,  but  it  may  also  have  been 
right,  since  the  times  really  may  have  been  the  same.  But 
in  this  other  case  when  we  compared  several  groups  of  indi- 
viduals and  said  that  the  members  of  one  were  so  much 
heavier  for  their  age  than  the  members  of  another,  our  con- 
clusion was  certainly  wrong,  since  there  is  every  reason  for 
believing  that  the  average  ages  of  the  members  of  the  differ- 
ent groups  were  not  at  all  the  same.  When  the  investigator 
compared  the  average  weight  of  all  the  boys  of  one  age  with 
that  of  all  the  boys  of  another  he  had  a  perfect  right  to  take 
the  age  of  each  individual  very  much  more  roughly  than  he 
would  have  done  if  he  had  been  comparing  two  individual 
boys,  because  he  had  good  reason  to  believe  that  the  in- 
accuracies would  balance  each  other.  In  this  the  method 
of  group  comparisons  has  a  great  advantage.  But  the  very 
fact  that  the  inaccurate  measurements  were  good  enough  for 
one  set  of  comparisons  made  him  take  for  granted  that  they 
were  good  enough  for  another.  Thus  the  peculiar  advantage 
possessed  by  this  method  of  group  comparisons  may  conceal 
a  great  danger. 


CHAPTER  XXXI. 

MEANS,  OR  AVERAGES. 

IN  the  last  chapter  we  had  occasion  to  show  how  an  infer- 
ence could  be  based  upon  a  comparison  of  averages.  Aver- 
ages are  used  so  much  in  various  kinds  of  reasoning  that  a 
few  definite  statements  should  be  made  about  them. 

"The  first  vague  notion  of  an  average,  as  we  now  under- 
stand it,  seems  to  me  to  involve  little  more  than  that  of  a 
something  intermediate  to  a  number  of  objects.  The  objects 
G  ,  must  of  course  resemble  each  other  in  certain 

conception.  respects.  Otherwise  we  should  not  think  of 
classifying  them  together;  and  they  must  also  differ  in 
certain  respects,  otherwise  we  should  not  distinguish  between 
them.  What  the  average  does  for  us,  under  this  primitive 
form,  is  to  enable  us  conveniently  to  retain  the  group  to- 
gether as  a  whole.  That  is,  it  furnishes  a  sort  of  representa- 
tive value  of  the  quantitative  aspect  of  the  things  in  question, 
which  will  serve  for  certain  purposes  to  take  the  place  of  any 
single  member  of  the  group."*  In  this  respect  an  average  is 
somewhat,  though  not  precisely,  like  a  general  name.  "The 
ordinary  general  name  rests  upon  [i.e.,  is  used  to  mark]  a 
considerable  variety  of  attributes,  mostly  of  a  qualitative 
character,  whereas  the  average,  in  so  far  as  it  serves  the  same 
sort  of  purpose,  rests  rather  upon  a  single  quantitative  attribute. 
It  directs  attention  to  a  certain  kind  and  degree  of  magnitude. 

*  John  Venn,  li  The  Logic  of  Chance  ",  1888,  pp.  436  fT. 

312 


VARIOUS   KINDS.  313 

"We  can  easily  see  that  the  number  of  possible  kinds  of 
average,  in  the  sense  of  intermediate  values,  is  very  great ; 
is,  in  fact,  indefinitely  great.  Out  of  the  general  conception 
of  an  intermediate  value,  obtained  by  some  treatment  of  the 
original  magnitudes,  we  can  elicit  as  many  subdivisions  as 
we  please,  by  various  modes  of  treatment.  There  are,  how- 
ever, only  three  or  four  which  for  our  purposes  need  to  be 
taken  into  account. 

"  In  the  first  place  there  is  the  arithmetical  average  or 
mean.  The  rule  for  obtaining  this  is  very  simple  :  add  all 
the  magnitudes  together,  and  divide  the  sum  by  their  number. 
This  is  the  only  kind  of  average  with  which  the  unscientific 
mind  is  thoroughly  familiar.  But  we  must  not  let  this  sim- 
plicity and  familiarity  blind  us  to  the  fact  that  there  are  defi- 
nite reasons  for  the  employment  of  this  average,  and  that  it 
is  therefore  appropriate  only  in  definite  circumstances." 

The  Arithmetical  Mean  of  a  series  of  quantities  is  that 
quantity  which  can  be  substituted  for  each  one  of  them  when 
they  are  to  be  added  together,  and  produce  the  same  sum. 
Six  is  the  arithmetical  mean  of  4,  5,  7,  8,  varions 
because  the  sum  of  these  four  numbers  and  the  kinds- 
sum  of  four  sixes  is  the  same.  Hence  "for  many  of  the 
ordinary  purposes  of  life,  such  as  purchase  and  sale,  we 
come  to  exactly  the  same  result,  whether  we  take  account 
of"*  the  exact  size  of  each  separate  quantity  and  the  differ- 
ences between  them,  or  suppose  each  one  of  them  to  be  equal 
to  the  average.  If  we  are  paying  for  melons  by  the  pound  it 
makes  no  difference  in  the  price  whether  the  dealer  says  that 
we  bought  one  which  weighed  4  pounds,  one  which  weighed  5, 
one  which  weighed  7,  and  one  which  weighed  8,  or  whether 
he  says  we  bought  four  that  weighed  about  6  pounds  apiece. f 

The  next  kind  of  mean,  or  average,  to  be  considered  is  the 
Geometrical.  It  is  that  quantity  which  can  be  substituted 

*  John  Venn,  loc.  cit. 

f  The  arithmetical  mean  is  the  simplest  case  of  the  mean  which  is 
obtained  by  the  method  of  least  squares. 


314  MEANS,  OR   AVERAGES. 

for  each  one  of  several  quantities  when  they  are  multiplied 
together,  and  give  the  same  product.  In  this  way  4  is  the 
mean  between  2  and  8,  for  we  get  16  whether  we  multiply  2 
by  8  or  4  by  4.  In  the  same  way  6  is  the  geometrical  mean 
of  2,  4,  27.  The  rule  for  finding  the  geometrical  mean  be- 
tween any  number  (w)  of  quantities  is  to  multiply  all  the 
quantities  together  and  find  the  «th  root  of  the  product.* 

Whether  in  any  case  we  should  use  an  arithmetical  or  a 
geometrical  mean  depends  altogether  upon  the  relations  which 
we  are  considering  between  the  things  in  question.  If  they 
are  merely  added  together  to  produce  an  external  result,  like 
weights  in  the  pan  of  a  balance  or  like  the  simple  interest 
which  different  sums  of  money  earn  in  the  same  year,  then  it 
is  clear  from  the  definition  of  the  arithmetical  mean  that  we 
should  use  it ;  but  if  the  quantities  are  thought  of  as  bearing 
some  fixed  ratio  to  each  other  and  depending  upon  each 
other  like  the  earnings  of  a  sum  of  money  from  year  to  year 
at  compound  interest,  then  it  is  clear  from  the  definition  that 
we  should  use  the  geometrical.  If  it  is  not  certain  what  the 
essential  relations  in  question  really  are,  then  it  is  not  certain 
which  mean  should  be  chosen.  In  the  ten  years  from  1890  to 
1900  the  population  of  Cleveland  increased  from  261,353  to 
381,768.  That  is,  it  gained  120,415  people,  or  a  trifle  over 
46$.  Shall  we  take  the  arithmetical  mean,  and  say  that  this 
represents  an  average  increase  each  year  of  12,041;  or  shall 
we  take  the  geometrical,  and  say  that  it  represents  an  average 
increase  each  year  of  3.86^?  The  two  means  are  quite  dif- 
ferent. If  we  take  the  arithmetical,  we  think  of  an  addition 
of  precisely  the  same  number  of  inhabitants  each  year;  if  we 

*  The  geometrical  mean  of  two  quantities  is  often  defined  as  '  a 
mean  proportional  between  them  ',  or  that  quantity  which  hears  the 
same  proportion  to  the  one  as  the  other  hears  to  it.  According  to  this 
definition  4  is  the  mean  between  2  and  8,  because  2:41:4:  8,  —  not  he- 
cause  2X8  =  4X4-  Mathematically  the  two  definitions  amount  to 
the  same  thing  ;  but  the  one  given  in  the  text  is  better  for  the  purposes 
of  logic. 


VARIOUS   KINDS.  315 

take  the  geometrical,  we  think  of  a  considerably  smaller  abso- 
lute addition  (viz.,  10,088)  in  the  first  year  of  the  ten,  when  the 
city  is  comparatively  small,  than  in  the  last  year  of  the  ten 
(viz.,  14,159),  when  it  is  considerably  larger.  Which  mean 
we  should  choose  is  simply  a  question  of  which  we  believe 
will  best  represent  the  facts.  If  the  growth  of  cities  depended 
altogether  upon  the  birth  of  children  within  their  boundaries, 
we  should  naturally  choose  the  geometrical  mean,  for  the 
larger  the  city  (other  things  being  equal)  the  more  children 
will  be  born  in  it.  If,  on  the  other  hand,  the  population 
of  a  city,  like  that  of  a  prison  or  a  hospital,  were  made  up 
altogether  of  certain  kinds  of  people  who  were  sent  there  from 
without,  there  would  be  no  reason  why  a  large  city  should 
gain  more  inhabitants  than  a  small  one  ;  and  the  more  appro- 
priate average  would  be  the  arithmetical.  With  most  cities 
the  natural  rate  of  growth  is  only  partly  geometrical  and  only 
partly  arithmetical;  so  that  neither  a  series  of  means  of  the 
one  sort  nor  a  series  of  the  other  would  give  a  wholly  satis- 
factory representation  of  the  mean  growth  from  year  to  year 
between  one  census  and  another.  If  in  any  case  or  set  of 
cases  we  have  reason  to  believe  that  the  true  mean  lies  some- 
where between  the  arithmetical  and  the  geometrical,  and  if 
we  wish  to  represent  the  facts  as  accurately  as  they  can  be 
represented  by  any  mean,  we  must  make  a  mean  that  does  lie 
between  the  two.* 

For  many  purposes  the  best  mean  to  choose  is  not  an  aver- 

*  In  estimating  the  population  for  any  given  time  on  the  basis  r  f  a  ?et 
of  census  returns  mathematicians  actually  use  a  set  of  equations  like 
this:  />  =r  a  -j-  bt  -j-  ct 2  -f-  dt  •"  -f-  etc.,  where  />  is  the  population  at  some 
given  time  (different  in  the  different  equations),  and  /  is  the  number  of 
units  of  time  (e.g.,  decennial  periods)  from  any  starting-point  to  the  time 
of  the  population/.  The  values  of  a,  />,  f,  d,  etc.,  are  found  from  these 
equations,  in  which  the  value  of  p  is  known,  by  the  method  of  least 
squares;  and  then  the  value  of/  at  any  other  time  can  easily  be  calcu- 
lated. 

This  formula  actually  does  represent  a  rate  of  increase  lying  some, 
where  between  an  arithmetical  and  a  geometrical  progression. 


316  MEANS,  OR    AVERAGES. 

age  in  any  mathematical  sense  of  the  word  at  all,  but  simply 
the  size  or  kind  that  occurs  most  frequently.  This  is  what 
is  generally  meant  by  the  '  average  man  '.  When  we  say  that 
the  average  man  likes  a  certain  kind  of  newspaper  or  a  certain 
kind  of  play,  we  simply  mean  that  the  people  who  like  that 
kind  of  newspaper  or  that  kind  of  play  are  more  numerous 
than  the  people  who  like  any  other  kind.  It  does  not  mean 
that  half  the  people  in  the  community  like  something  more 
refined  or  more  intellectual  and  that  the  other  half  like  some- 
thing less  refined  or  intellectual.  The  '  average  man '  may 
happen  to  lie  midway  between  t\vo  extremes;  but  it  is  the 
numerousness  of  such  men,  not  their  middle  position  or  any 
other  such  relation  to  other  kinds  of  men,  that  the  editor  or 
the  playwright  cares  about.  This  average  is  the  '  Mode'. 

Another  kind  of  average,  which  is  often  quite  good  enough 
to  represent  a  group  for  the  purpose  of  comparing  it  with 
some  other  group,  is  what  Mr.  Galton  calls  the  '  Median  '.  If 
we  suppose  all  the  objects  in  a  group  to  be  arranged  in  a  row 
according  to  their  size,  the  median  size  is  the  si/e  of  the 
middle  object  in  the  row.  If  \ve  have  to  compare  the  six.e  of 
the  soldiers  in  an  American  regiment  with  that  of  the  sol- 
diers in  a  Japanese  regiment,  we  can  measure  all  the  men  in 
each  and  take  the  arithmetical  mean,  if  we  wish  to  ;  but  it 
would  be  much  easier  and  it  would  answer  the  purpose  quite 
as  well  to  take  the  middle-sized  man  from  each  regiment  and 
compare  the  two.  The  men  in  the  middle  make  a  better  basis 
of  comparison  between  the  two  regiments  than  those  at  either 
end,  because  the  size  of  the  men  who  happen  to  be  in  that 
position  is  not  affected  so  much  by  chance.  In  two  regi- 
ments raised  in  the  same  place  and  in  the  same  way  the  two 
men  of  middle  size  would  be  almost  exactl v  of  the  same 
height  ;  but  the  men  of  extreme  size  might  not,  for  one 
regiment  might  happen  to  contain  a  giant  or  a  dwarf  and 
the  other  not. 

Averages,  or  means,  can  be  used  for  three  distinct  pur- 
poses, some  of  which  have  been  referred  to  already. 


FIRST   USE   OF   AVERAGE.  317 

Averages  can  be  used,  in  the  first  place,  to  settle  the  con- 
flicting claims  of  a  number  of  different  measurements  of  the 
same  quantity.  When  we  try  to  measure  a  thing  FJrst  use 
very  accurately  we  usually  take  the  measurement  of  average. 
at  least  twice,  and  when  we  come  to  compare  the  t\vo  or 
more  measurements  we  always  find,  however  carefully  they 
have  been  taken,  that  there  is  some  slight  difference  between 
them.  This  is  true  when  we  try  to  measure  the  side  of  a 
room  to  an  eighth  of  an  inch  with  an  ordinary  foot-rule,  and 
it  is  true  of  the  extremely  careful  measurements  made  with 
the  best  possible  apparatus  in  a  physical  laboratory.  Indeed, 
the  more  accurate  we  try  to  be,  the  more  of  these  discrep- 
ancies \ve  shall  notice.  In  a  case  of  this  sort  the  chances 
are  that  any  measurement  which  we  accept  as  the  true  one 
will  be  wrong;  but  with  this  probability  of  being  wrong,  it 
is  valuable  to  have  a  reasonable  assurance  that  we  are  not 
very  far  wrong.  Suppose  that  there  have  been  ten  measure- 
ments and  that  the  smallest  is  1038  and  the  largest  1043.  If 
we  arbitrarily  chose  either  of  these  extreme  measurements 
as  the  one  to  go  by,  and  if  the  measurement  at  the  other 
extreme  really  happened  to  be  right,  then  we  should  have 
made  a  blunder  of  5  units;  if,  on  the  other  hand  we  chose 
some  number  about  half  way  between  them  as  the  true  meas- 
urement, then,  if  either  of  the  extreme  measurements  were 
correct,  the  error  would  not  exceed  two  or  three  units,  and  if 
the  real  quantity  should  lie  between  the  two  extremes,  then,  of 
course,  the  error  would  be  still  less.  Thus,  if  we  are  recon- 
ciled to  an  error  in  our  measurement  but  wish  a  reasonable 
assurance  that  the  error  is  small,  it  is  usually  better  to  choose 
some  kind  of  a  mean  measurement  than  one  of  the  extremes.* 

*  There  are  three  principles  which  can  be  taken  for  granted  when  \ve 
try  to  find  the  true  value  of  a  quantity  from  a  series  of  different  measure- 
ments: (I)  Positive  and  negative  errors  are  equally  probable;  (2)  There 
will  always  be  more  small  errors  than  large  ones;  (3)  Very  large  errors 
do  not  occur  at  all.  To  explain  this  last  point.  If  I  am  measuring  a 
wall  with  a  yardstick  and  the  record  shows  that  according  to  each  of  the 


318  MEANS,  OR   AVERAGES. 

I  say  '  usually  '  because  it  is  only  usually  that  it  is  better. 
Choosing  the  mean  is  no  infallible  rule  for  getting  certainty 
out  of  uncertainty  ;  and  sometimes  the  blunderer  who  ac- 
cepts the  first  measurement  that  he  takes  conies  nearer  to  the 
truth  than  the  careful  man  who  finds  the  mean  of  a  large 
number. 

To  take  the  mean  of  several  estimates  is  a  rule  that  might 
very  well  be  carried  farther  than  it  is  into  every-day  life. 
Too  often  we  are  guided  by  our  last  impressions,  not  because 
we  have  any  reason  to  believe  that  the  last  is  better  than  any 
other,  but  merely  because  it  is  the  one  which  is  present  at 
the  time  when  the  final  estimate  must  be  given.  A  teacher, 
for  example,  examines  a  piece  of  work  and  marks  it  5.  The 
next  day  he  examines  it  again  and  it  seems  to  be  worth  7. 
The  chances  are  that  this  is  the  mark  which  he  will  hand  in. 
What  he  should  do  under  the  circumstances  is  to  treat  him- 
self objectively ;  to  recognize  that  he  had  made  two  conflict- 
ing judgments ;  to  ask  whether  the  conditions  under  which 
they  were  made  were  any  more  favorable  in  the  one  case  than 
in  the  other  ;  and,  if  they  were  not,  to  split  the  difference 
between  them  and  mark  the  work  6.  It  is  not  true  that  '  first 
impressions  are  always  the  best '  ;  but  the  saying  would  never 
have  come  into  existence  if  people  had  not  often  blundered 
by  ignoring  them  altogether. 

first  four  measurements  it  is  somewhere  between  102  feet  3  inches  and 
102  feet  4^  inches,  while  according  to  the  record  for  the  fifth  measure- 
ment it  is  104  feet  3J  inches,  it  is  perfectly  evident  that  this  last  record 
is  wrong.  It  could  not  have  been  produced  by  any  combination  of 
'errors'  (such  as  slight  variations  in  the  length  of  the  measuring- 
stick,  in  the  accuracy  with  which  it  is  placed  and  read,  etc.).  It  is 
simply  a  mistake: — I  wrote  flown  the  wrong  figure,  or  I  made  a  mistake 
in  my  counting — and  if  it  is  not  clear  how  the  record  can  be  corrected, 
the  measurement  must  be  disregarded. 

It  is  in  accordance  with  all  three  of  these  principles  that  the  mean  is 
not  only  a  safer  measurement  to  accept  than  either  extreme,  as  I  have 
stated  in  the  text,  but  also  that  it  is  far  more  likely  to  be  substantially 
correct,  though  of  course  it  is  riot  certain  to  be. 


FIRST   USE   OF   AVERAGE.  319 

Taking  the  mean  of  several  measurements  is  not  always 
the  best  way  to  find  a  quantity.  In  the  first  place,  it  is 
useless  to  take  the  mean  of  several  measurements  unless  we 
can  put  up  with  the  amount  of  error  which  such  a  proceed- 
ing will  necessarily  or  probably  involve.  This  error  may  be 
the  one  which  is  calculated  from  the  differences  between  the 
individual  measurements;  it  may  be  some  constant  error 
which  probably  exists  and  affects  all  the  measurements,  but 
for  which  we  cannot  make  proper  allowance  because  we  do 
not  know  its  amount  and  direction  ;  or  a  combination  of  them 
both.  In  the  second  place,  we  must  not  take  the  average 
of  a  set  of  measurements  if  we  wish  results  which  are  as 
accurate  as  possible  and  if  the  measurements  were  taken 
carelessly  and  it  is  possible  to  take  them  over  again  more 
accurately.  Finally,  we  must  not  take  the  average  if  we- 
believe  that  there  was  some  cause  at  work  which  prevented 
the  errors  from  being  scattered  fairly  evenly  in  both  direc- 
tions, so  long,  at  least,  as  there  is  any  possibility  of  judging 
which  direction  ihe  errors  tended  to  take.  We  must  not 
choose  a  mean  between  the  measurements  given  by  two 
individuals  if  we  have  reason  to  believe  that  one  of  them  is 
dishonest  or  incapable,  and,  on  the  same  principle,  we  must 
not  choose  the  mean  of  several  measurements  if  we  have  any 
reason  to  believe  that  the  more  skilfully  a  measurement  is 
taken  the  more  it  approaches  to  one  of  the  extremes.  "  In 
endeavoring  to  obtain  a  correct  estimate  of  the  apparent 
diameter  of  the  brightest  fixed  stars,  we  find  a  continuous 
diminution  in  estimates  as  the  powers  of  observation  in- 
creased. Kepler  assigned  to  Sirius  an  apparent  diameter  of 
240  seconds;  Tycho  Brahe  made  it  126;  Gassendi,  10 
seconds;  Galileo,  Helvetius,  and  J.  Cassini,  5  or  6  seconds. 
Halley,  Michell,  and  subsequently  Sir  W.  Herschel  came  to 
the  conclusion  that  the  brightest  stars  in  the  heavens  could 
not  have  real  discs  of  a  second,  and  were  probably  much  less 
in  diameter.  It  would  of  course  be  absurd  to  take  the  mean 
of  quantities  which  differ  more  than  240  times;  and  as  the 


320  MEANS,  OR   AVERAGES. 

tendency  has  always  been  to  smaller  estimates,  there  is  a 
considerable  presumption  in  favor  of  the  smallest."  * 

The  second  use  of  averages  is  to  find  the  individual  which 
best  serves  as  a  type  or  representative  of  the  species  to  which 
it  belongs.  In  the  case  of  averages  like  those  that  we 
Second  use  have  just  considered  there  was  one  true  quantity 
of  average,  -which  we  were  trying  to  find.  In  this  case  there 
are  many  individuals  of  a  given  kind,  each  with  a  quantity 
of  its  own,  and  we  wish  to  pick  out  one  that  will  represent 
them  all.  A  type  of  this  sort  is  often  doubly  valuable;  for 
in  many  cases  (as  with  natural  species)  an  individual  lying 
about  half  way  between  the  t\vo  extremes  is  not  only  a  fairly 
good  representative  of  each  of  them,  but  is  also  an  excellent 
representative  of  a  majority  of  the  whole  species,  because 
men  or  horses  or  cats  of  medium  size  are  very  much  more 
common  than  the  very  large  ones  or  the  very  small  ones. 
If  a  large  number  of  men  be  arranged  in  a  row  according  to 
their  height,  a  line  that  just  touched  the  tops  of  their  heads 
would  be  about  the  shape  of  the  black  line  on  the  next 
page. f  There  would  be  much  more  difference  between  the 
very  tall  man  or  the  very  short  man  at  one  end  of  the  line 
and  the  man  next  to  him  than  between  any  two  successive 
men  near  the  middle  of  the  line. 

The  reason  for  this  is  easily  explained.  Suppose  that 
there  are  ten  independent  variables  which  together  deter- 
mine a  man's  height;  e.g.,  the  height  of  his  father  as  com- 
pared with  the  average  of  the  species,  that  of  his  mother, 

*  "Principles  of  Science",  p.  390. — Instead  of  rejecting  the  poorer 
measurements  entirely  physicists  sometimes  'weight'  tlicm,  or  admit 
them  into  the  final  reckoning  in  such  a  way  that  they  do  nut  atiect  it 
very  much.  Wh.it  weights  are  to  be  attached  to  the  various  measure- 
ments— whether  A's  shall  count  fur  half  as  much  as  li's  or  oirvf^r  a 
tenth  as  much — lias  to  he  determined  arbitrarily,  though  there  is  a 
definite  rule  for  determining  the  weights  when  they  are  made  to  depend 
wholly  upon  the  number  and  probable  error  of  the  measurements  in  each 
of  the  series  to  be  combined. 

|  After  Huwditch.  '-(irowth  of  Children  ",  etc.  22(1  An  Report 
of  the  State  Board  of  Health  of  Mass. 


SECOND   USE   OF   AVERAGE. 


321 


his  own  health  during  the  period  of  growth,  his  food  during 
that  period,  the  amount  of  outdoor  life  which  he  had,  the 
amount  and  regularity  of  his  sleep,  etc.  Let  us  represent 
these  different  conditions  by  different  letters  from  A  to  J; 
let  us  suppose  for  the  sake  of  simplicity  that  each  of  these 
conditions  is  either  distinctly  favorable  or  distinctly  un- 


favorable; that  each  condition  is  as  likely  to  be  favorable  as 
to  be  unfavorable;  and  that  one  favorable  or  unfavorable 
condition  counts  for  as  much  as  another.  Condition  A  will 
be  favorable  in  one  case  out  of  two;  and  in  cases  when  A  is 
favorable  B  will  be  favorable  in  one  out  of  two.  That  is  to 
say,  A  and  B  will  both  be  favorable  in  only  one  case  out  of 
four.  Similarly  they  will  both  be  unfavorable  in  only  one 
case  out  of  four.  But  in  one  case  out  of  four  A  will  be 
favorable  and  B  unfavorable,  and  in  one  case  out  of  four  A 
will  be  unfavorable  and  B  favorable.  Hence  with  only  two 
variables  there  is  one  case  out  of  four  when  both  conditions 
are  good ;  one  when  both  are  bad  ;  and  two  when  one  is  good 
and  the  other  is  bad.  Working  the  problem  out  in  this  way 
we  find  that  all  ten  conditions  are  favorable  (or  unfavorable) 
in  only  one  case  out  of  210,  i.e.,  in  i  out  of  1024;  but  that 
cases  in  which  some  of  the  conditions  are  favorable  and 
others  unfavorable  occur  much  oftener,  and  that  the  more 
evenly  the  favorable  and  unfavorable  conditions  are  divided 


322  MEANS,  OR  AVERAGES. 

the  more  frequently  does  the  combination  occur.      Out  of 

1024  cases 

10  conditions  are  favorable     i  time. 

9          "  "  "          10  times. 

8          "  "  "         45 

7          "  "  "        120      " 

6          "  "  "       210      " 

C  "  "  '  '  ->    -    7  '  ' 

4          "  "          "        210      " 

3  "  "  "  120          " 

2          "  "          "         45      " 

I  "  "  "  JO         " 

o          "  "          "  i       " 

To  students  acquainted  with  the  binomial  theorem  these 
figures  and  the  process  by  which  they  are  reached  will  be 
familiar.  The  mathematical  law  on  which  they  are  based 
represents  the  facts  in  most  cases  well  enough  to  show  how 
much  more  frequently  things  of  medium  size  or  quality  are 
produced  than  those  at  either  of  the  extremes.  Thus  the 
man  of  medium  size  or  attainments  is  usually  the  'average 
man  '  in  two  or  even  three  senses  of  the  words.  He  is  the 
man  who  stands  in  about  the  middle  of  the  line;  he  is  the 
commonest  kind  of  man;  and  very  likely  the  number  that 
expresses  his  size  or  attainments  is  nearly  the  arithmetical 
mean  of  the  numbers  which  express  the  size  or  attainments 
of  all  those  in  the  group. 

Before  we  have  a  right  to  expect  the  arithmetical  mean 
or  the  median  of  a  group  to  be  the  commonest  size  or  kind 
found  in  that  group  we  must  make  sure  that  we  are  really 
dealing  with  one  group  of  homogeneous  things  and  not  with 
several.  If  we  measure  a  group  of  men  half  of  whom  are 
Americans  and  the  other  half  African  pygmies,  the  average 
height  will  be  too  small  for  the  Americans  and  too  large  for 
the  pygmies;  and  it  might  well  be  that  not  a  single  man  in 
the  whole  complex  group  came  anywhere  near  it.  In  the 
same  way,  if  we  should  find  the  average  size  of  all  the  articles 


SECOND   USE  OF   AVERAGE.  323 

in  a  given  room,  from  tables  and  lounges  to  pins  and  collar- 
buttons,  there  is  no  reason  to  think  that  things  the  size  of 
the  average — even  if  such  things  existed — would  be  any. 
more  common  than  things  of  any  other  size  that  any  one 
might  happen  to  think  of.  The  things  in  the  room  are  not 
homogeneous;  and  neither  are  the  Americans  and  pygmies. 
To  be  homogeneous,  in  the  sense  in  which  the  word  is  used 
here,  things  must  be  of  the  same  general  kind, — i.e. ,  pro- 
duced by  essentially  similar  groups  of  causes, — and  the 
differences  between  them  must  be  the  '  compounded  '  result 
of  a  large  number  of  relatively  independent  conditions  of 
approximately  equal  value.  The  articles  in  the  room  were 
not  of  the  same  kind  at  all;  and  in  the  case  of  the  Ameri- 
cans and  the  pygmies  the  one  condition  of  ancestry,  different 
for  the  two  groups,  overshadowed  all  the  rest. 

Even  when  the  members  of  a  group  are  perfectly  homo- 
geneous it  does  not  always  follow  that  those  of  medium  size 
or  attainments  are  the  most  numerous.  In  a  previous  para- 
graph I  said  that  in  a  regiment  of  soldiers  arranged  in  line 
according  to  their  height  there  might  be  a  giant  at  one  end 
of  the  line  and  a  dwarf  at  the  other.  But  if  the  soldiers  are 
regular  infantrymen  recruited  in  time  of  peace,  the  dwarf 
would  not  be  there,  simply  because  the  government  refuses 
to  accept  recruits  under  a  certain  height.  The  well-marked 
curve  at  one  end  of  the  line  which  touches  the  men's  heads 
is  thus  cut  off,  and  in  a  regiment  recruited  in  this  way  the 
commonest  type  of  man  would  therefore  be  a  little  to  the 
small  side  of  the  median  and  a  little  smaller  than  the 
arithmetical  mean.  So  in  any  class  at  school  or  college,  the 
students  who  are  laziest  and  most  stupid  have  been  cut  off 
by  previous  examinations;  and  consequently  at  the  lower 
end  of  the  class  we  do  not  find  one  person  of  extraordinary 
ineffectiveness,  but  rather  a  fairly  large  group  who  have 
barely  succeeded  in  fulfilling  the  minimum  requirements. 
Here  also,  therefore,  the  largest  group  is  towards  the  lower 
end  and  somewhat  below  the  arithmetical  average. 


324  MEANS,  OR   AVERAGES. 

Another  thing  we  must  be  careful  about  with  averages  of 

this  sort  is  not  to  mistake  the  average  for  the  ideal.  If  a 
child's  growth  is  not  up  to  the  average,  the  physician  has  a 
right  to  suspect,  though  perhaps  not  to  conclude,  that 
something  is  wrong;  but  then  the  average  by  which  the 
physician  is  guided  is  an  average  of  children  in  good  health, 
and  then  again  it  is  only  when  the  child's  weekly  growth 
falls  below  the  average — not  above  it — that  the  physician  is 
anxious.  Thus  he  regards  the  average  growth  as  a  kind  of 
minimum — not  as  the  maximum  to  be  striven  for.  So  also 
with  matters  of  conduct,  the  fact  that  '  everybody  '  does  a 
certain  kind  of  thing  is  no  reason  in  the  world  for  believing 
that  that  is  an  ideal  kind  of  thing  to  do.  In  the  case  of  a 
race  perfectly  adjusted  to  its  environment  and  incapable  of 
further  improvement  it  might  be;  but,  as  things  stand,  the 
commonplace  of  to-day  is  the  ideal  of  yesterday,  and  the 
ideal  of  to-day  is  the  commonplace,  not  of  to-day,  but  of 
to-morrow.  Another  reason  for  striving  for  something 
better  than  the  average  in  the  case  of  conduct  is  this:  The 
average  is  made  up  of  good,  bad,  and  indifferent;  and  if  the 
best  people  m  a  community  should  suddenly  cease  to  keep 
as  far  above  the  average  as  the  bad  are  below  it,  the  average 
would  necessarily  fall,  and  would  keep  on  falling  until  the 
community  went  to  pieces  or  until  some  one  arose  again 
who  was  willing  to  be  better  than  the  average  of  his  fellows. 

The  third  purpose  for  which  we  find  a  mean  is  convenience 
in  representation — to  have  "  a  merely  representative  num- 
Thirduse  her,  expressing  the  general  magnitude  of  a  series 
oi  average.  Qf  quantities,  and  serving  as  a  convenient  mode 
of  comparing  them  with  other  series  of  quantities",  as  in 
group  comparisons.  "  Such  a  number  is  properly  called  the 
fictitious  mean  or  the  average  result. ' '  * 

The  average  weight  of  tlu  players  in  a  football  team  may 

*  YV.  S.  Jevons,  "Principles  of  Science  "  (1887).  p.  359.  The  dis- 
tinction which  Jevons  here  makes  between  the  u^e  of  the  words  Mean 
and  Average  is  not  always  observed,  and  I  have  ignored  it  in  the  text. 


THIRD   USE  OF  AVERAGE.  325 

not  come  anywhere  near  the  weight  of  any  one  of  them,  and 
it  is  not  a  kind  of  type  towards  which  football-players  tend; 
for  there  is  reason  why  the  quarter-backs  should  usually  be 
lighter  and  the  centres  heavier.  There  is  therefore  no  one 
thing  in  the  world  which  the  mean  employed  in  this  way 
represents  or  attempts  to  represent,  and  yet  it  has  a  real  use 
when  we  consider  the  group  as  a  whole  in  its  relations  to 
something  beyond :  in  this  case  in  relation  to  some  other  foot- 
ball team  and  the  chance  of  beating  it.  So  when  we  give 
the  mean  temperature  of  Winnipeg  we  do  not  mean  to  say 
that  that  is  the  commonest  temperature  there,  nor  yet  that 
that  is  a  kind  of  type  which  the  temperature  of  each  day 
naturally  tends  to  approach;  for  we  know  that  most  days  are 
either  hotter  or  colder  and  that  it  is  natural  for  days  to  be 
much  hotter  in  summer  and  much  colder  in  winter.  But 
with  reference  to  places  and  relations  that  lie  beyond,  a 
statement  of  the  average  temperature  may  be  full  of  mean- 
ing. If  the  mean  temperature  of  Winnipeg  is  lower  than 
that  of  San  Francisco,  this  means  that  for  some  reason  or 
other  it  receives  less  heat  from  the  sun  in  the  course  of  a  year, 
or  radiates  more  away,  or  perhaps  both;  and  if  there  is  any 
process  of  growth  or  manufacture  which  depends  upon  the 
total  amount  of  heat  (regardless  of  variations  from  day  to 
day)  which  Nature  gives  in  the  course  of  a  whole  year,  a 
knowledge  of  the  mean  temperature  of  each  place  would 
tell  which  of  the  two  would  be  the  more  favorable  in  this 
respect.  To  quote  again  from  Jevons: 

"  Although  the  average  when  employed  in  its  proper  sense 
of  a  fictitious  mean  represents  no  really  existing  quantity, 
it  is  yet  of  the  highest  scientific  importance,  as  enabling  us 
to  conceive  in  a  single  result  a  multitude  of  details.  It 
enables  us  to  make  a  hypothetical  simplification  of  a  problem, 
and  avoid  complexity  without  committing  error.  The 
weight  of  a  body  is  the  sum  of  the  weights  of  infinitely  small 
particles,  each  acting  at  a  different  place,  so  that  a  mechan- 
ical problem  resolves  itself,  strictly  speaking,  into  an  infinite 


326  MEANS,  OR   AVERAGES. 

number  of  distinct  problems.  We  owe  to  Archimedes  the 
first  introduction  of  the  beautiful  idea  that  one  point  may 
be  discovered  in  a  gravitating  body  such  that  the  weight  of 
all  the  particles  may  be  regarded  as  concentrated  in  that 
point,  and  yet  the  behavior  of  the  whole  body  will  be 
exactly  represented  by  the  behavior  of  this  heavy  point. 
This  Centre  of  Gravity  may  be  within  the  body,  as  in  the 
case  of  a  sphere,  or  it  may  be  in  empty  space,  as  in  the  case 
of  a  ring.  Any  two  bodies,  whether  connected  or  separate, 
may  be  conceived  as  having  a  centre  of  gravity,  that  of  the 
sun  and  earth  lying  within  the  sun  and  only  267  miles  from 
its  centre. "  * 

While  averages  of  this  sort  can  represent  the  individuals 
in  a  group  for  certain  purposes,  it  is  only  as  members  of  the 
group.  The  average  weight  of  the  men  in  any  athletic  team 
is  nothing  more  than  the  figure  obtained  by  dividing  the 
total  weight  by  the  number  of  players.  The  minute  any  one 
of  them  leaves  the  team  that  average  ceases  absolutely  to 
represent  him  in  any  way  whatever,  and  ceases  at  the  same 
instant  to  represent  the  others  either,  whether  individually 
or  collectively.  An  average  of  this  sort  need  not  be  in  any 
sense  either  a  representative  of  a  single  individual,  or  of  a 
type  towards  which  the  individuals  tend,  or  of  an  ideal. 
It  is  the  mere  product  of  an  arithmetical  process,  useful  for 
the  estimation  of  certain  outward  relations  of  the  things 
averaged. 

The  term  Expectation  of  Life  as  used  in  insurance  is  likely 
to  lead  to  the  confusing  of  the  two  ideas  which  we  are  here 
trying  to  distinguish.  To  the  insurance  company  it  means 
merely  the  average  time  that  insurable  people  of  a  given  age 
and  sex  continue  to  live.  To  the  layman  it  is  likely  to  mean 
the  time  that  he,  as  an  individual,  will  probably  continue  to 
live — a  very  different  thing,  which  should  be  calculated  in 
an  entirely  different  way. 

*Jevons,  op.  cit.,  pp.  363-4. 


MEASURES   OF   ERROR.  327 

Often  it  is  well  to  add  to  an  average  some  indication  of 
the  accuracy  with  which  the  average  represents  the  quantities 
whose  average  it  is.  Ten  is  the  arithmetical  Measures  of 
mean  between  9  and  u.  It  is  also  the  arith- 
metical mean  between  5  and  15.  But  in  the  first  case  the 
average  comes  much  nearer  to  each  of  the  separate  quan- 
tities than  in  the  second.  In  the  first  case  the  difference 
between  the  average  and  each  of  the  quantities  averaged  is 
only  i  ;  in  the  second  it  is  5.  When  the  average  represents 
a  large  number  of  quantities,  the  simplest  measure  of  the  dif- 
ference between  it  and  each  one  of  the  quantities  averaged  is 
the  average  variation  of  the  separate  quantities  from  that  aver- 
age. The  arithmetical  average  of  the  variations  is  found  by 
finding  the  difference  between  the  average  and  each  one  of 
the  separate  quantities  (regardless  of  whether  that  quantity  be 
larger  than  the  average  or  smaller),  adding  all  these  differ- 
ences together,  and  dividing  by  the  total  number  of  quanti- 
ties. Thus  the  average  of  5,  6,  7,  n,  13,  8,  6,  20,  10,  14 
is  10  ;  the  separate  variations  from  the  average  are  respec- 
tively 5,  4,  3,  i,  3,  2,  4,  10,  o,  4;  the  sum  of  these  separate 
variations  is  36  ;  and  since  there  are  ten  quantities,  the  aver- 
age variation  is  3.6. 

When  we  are  dealing  with  a  number  of  separate  quantities 
a  knowledge  of  this  average  variation  enables  us  to  tell  to 
what  extent  the  average  may  be  regarded  as  representative  of 
each  of  them,  and  as  thus  serving  the  second  purpose  of  an 
average,  and  to  what  extent,  on  the  contrary,  it  must  be  re- 
garded as  a  purely  fictitious  quantity  serving  the  third  pur- 
pose only.  Of  course  the  smaller  the  average  variation  the 
more  accurately  the  average  represents  the  separate  quantities 
averaged. 

When  we  are  dealing  with  different  measurements  of  the 
same  quantity  the  average  variation  of  the  separate  measure- 
ments from  the  average  gives  a  measure  of  their  accuracy. 
To  be  sure  it  does  not  tell  anything  about  '  constant '  or 
'  systematic  '  errors  which  affect  all  the  measurements  in  the 


328  MEANS,  OR   AVERAGES. 

same  way;  but  it  does  tell  how  much  importance  must  be 
attached  to  '  accidental '  errors,  or  those  which  result  from  a 
large  number  of  different  causes  and  are  as  likely  to  affect  a 
measurement  in  one  direction  as  in  the  other.  The  larger 
the  average  variation,  the  more  important  are  these  '  acci- 
dental' errors  and  the  less  can  we  rely  upon  an  average 
derived  from  a  small  number  of  measurements. 

This  average  variation  is  easily  found,  and  it  is  a  good 
enough  measure  of  error  for  some  purposes  ;  but  mathe- 
maticians do  not  use  it.  What  they  do  use  is  either  the 
Median  Error — generally  known  as  the  'Probable  Error' — 
or  the  Mean  Square  Error.  The  former  is  commonly  used 
in  English-speaking  countries,  the  latter  in  Germany. 

The  Median  Error,  or  so-called  Probable  Error,  is  the 
variation  from  the  mean  that  half  the  separate  measurements 
fall  short  of  and  the  other  half  exceed.  If  \ve  suppose  all  the 
separate  measurements  to  be  arranged  in  order  of  magnitude, 
the  central  quantity  is  the  median,  and  the  Median  Error 
is  the  difference  between  that  central  quantity  and  the  quan- 
tity half-way  between  it  and  the  end  of  the  line  in  either 
direction.  The  '  Probable  Error  '  is  thus  the  amount  of  error 
that  any  one  of  the  quantities  is  as  likely  to  fall  short  of  as  to 
exceed.  It  is  not  the  amount  of  error  or  variation  from  the 
mean  that  will  probably  be  made.  If  we  denote  the  differ- 
ence between  each  individual  measurement  and  the  mean 
(i.e.,  the  'errors'  or  'residuals')  by  z\ ,  z>2,  v3 ,  etc.,  and  the 
total  number  of  measurements  by  n,  the  formula  for  finding 
the  Probable  Error  (;-)  of  a  single  observation  is  this: 


r  =  -6745  v-fa8  +  V?  +  ^  +  •  •  •  +  ^ 
or,  more  briefly, 


The  probable  error  of  the  mean,  ro ,  is  — -. 

Vn 


MEASURES   OF    ERROR,  329 

The  formula  for  the  Mean  Square  Error  of  a  single  meas- 
urement, e,  or  of  the  mean,  e0 ,  is  the  same  as  that  for  r  or 
r0,  except  that  the  factor  .6745  is  omitted. 

The  calculated  error  of  a  measurement  is  usually  written 
after  it,  thus:  1287  ±  3.  Unfortunately,  however,  this  is 
ambiguous,  for  sometimes  the  error  indicated  in  this  way  is 
the  error  of  any  one  measurement  out  of  a  series,  and  some- 
times it  is  the  error  of  the  mean.  By  giving  the  latter  where 
one  expects  the  former  an  observer  sometimes  makes  his  re- 
sults appear  more  accurate  than  they  really  are. 

The  student  who  wishes  a  fuller  treatment  of  this  subject 
is  referred  to  Venn's  "Logic  of  Chance",  to  Jevons' 
"  Principles  of  Science  ",  or  to  some  one  of  the  many  mathe- 
matical treatises  on  the  theory  of  probability,  such  as  Merri- 
man's  or  Comstock's. 


CHAPTER   XXXII. 
PROBABILITY. 

Ix  the  last  chapter  we  found  that  where  several  measure- 
ments or  estimates  do  not  agree  it  is  often  of  practical 
advantage  to  assume  that  the  truth  lies  somewhere  between 
Whv  them,  and  therefore  to  find  out  the  average.  We 

needed.  found,  however,  that  sometimes  the  nature  of  the 

case  is  such  that  an  average  is  out  of  the  question.  If  two 
people  both  claim  the  same  piece  of  land,  it  would  hardly  do 
to  say  that  each  of  them  owns  half  of  it;  if  one  toss  of  a 
penny  gives  heads  and  another  gives  tails,  there  is  no  prac- 
tical purpose  which  will  be  served  by  assuming  that  the 
natural  position  of  the  penny  is  neither  with  heads  up  nor 
with  tails  up,  but  on  its  edge;  if  we  do  not  know  whether  a 
certain  act  will  please  a  person  or  annoy  him,  it  will  hardly 
do  to  assume  that  it  will  do  neither  one  nor  the  other.  In 
cases  of  this  sort  the  mean  is  almost  sure  to  be  wrong,  and 
so  far  wrong  as  to  serve  no  practical  use;  it  is  therefore 
excluded  and  we  have  to  choose  between  the  extremes.  The 
theory  of  probability  discusses  this  choice. 

To  the  ordinary  human  mind  and  to  all  of  the  brutes  this 
choice  between  extremes  is  often  more  natural  than  the  search 
for  a  mean.  If  we  do  not  know  whether  to  fight  a  certain 
enemy  as  hard  as  we  can  or  to  run  a\vay  from  him  as  hard 
as  we  can,  it  is  usually  better  to  do  one  or  the  other — no 
matter  which — than  to  follow  the  middle  course  and  sit  still 
and  wait  to  be  devoured ;  and,  fashioned  as  we  are  for  the 

330 


WHAT    IT   IS   NOT.  331 

world  in  which  we  live,  it  is  more  likely  that  we  will.  If  a 
friend  is  accused  of  playing  us  false,  we  may  believe  the 
charge,  we  may  indignantly  reject  it,  or  we  may  alternate 
between  these  two  extremes;  but  we  are  not  likely  at  the 
time  to  assume  that  he  was  partly  true  and  partly  false  or  to 
take  an  attitude  of  perfectly  neutral  doubt.  We  are  natu- 
rally partisan,  and  even  when  we  seem  to  be  calmly  halting 
between  two  opinions  we  are  generally  not  halting  at  all,  but 
uncomfortably  oscillating  from  the  one  to  the  other.  Thus 
not  only  is  it  often  perfectly  rational,  but  it  is  also  perfectly 
natural,  to  choose  and  accept  as  true  some  one  of  several 
incompatible  alternatives,  and  it  is  the  business  of  a  logical 
theory  of  probability  to  show  the  kind  of  ground  on  which 
we  can  justify  the  choice  of  any  particular  one  to  the  exclu- 
sion of  the  rest. 

When  we  toss  a  penny  we  say  that  heads  and  tails  are 
equally  '  probable  '  or  equally  '  likely  ' — that  '  the  chances  ' 
are  even;  and  when  we  throw  dice  we  say  that  double  sixes 
is  '  improbable  '  or  '  unlikely  ' — that  '  the  chances  '  are 
against  it.  What  do  we  mean  by  these  words  '  probable  ' 
and  '  improbable  '  and  their  equivalents  ? 

Probability  has  sometimes  been  defined  as  a  measure  of 
belief.  According  to  this  definition,  when  we  say  that  the 
chances  are  nineteen  to  one  in  favor  of  a  certain  What  it 
event,  we  mean  that  we  have  some  expectation  isnot- 
of  its  happening  and  some  expectation  of  its  not  happening, 
but  that  the  expectation  of  its  happening  is  painted  nineteen 
times  as  vividly  upon  the  mind  as  the  expectation  of  its  not 
happening,  so  that  when  the  two  pictures  come  back  to  us 
the  one  has  nineteen  times  the  force  and  vivacity  of  the 
other.*  But  if  this  were  all  that  we  meant  by  probability, 
the  way  to  find  out  in  any  particular  case  what  the  chances 
or  probabilities  were  would  be  merely  to  examine  one's  own 

*  See  Hume's  "Treatise  of  Human  Nature",  Bk.  I.  Ft.  Ill,  Sec. 
XII. 


332  PROBABILITY. 

— or  some  one  else's — mind  and  compare  the  strength  of  its 
various  expectations.  This,  however,  is  not  what  we  do, 
or  rather  it  is  not  what  we  know  we  ought  to  do.  When 
we  want  to  get  at  the  probabilities  in  a  case  we  should 
examine  the  case,  not  our  own  feelings  about  it,  and  accept 
the  result  of  this  examination  whether  it  agrees  with  our 
feelings  or  not.  Of  course  we  cannot  examine  things  with- 
out having  thoughts;  but  probability  has  to  do,  not  with  the 
thoughts,  but  with  the  things. 

Probability  has  to  do  with  things;  and  yet  it  is  not  some 
mysterious  inward  power  that  strives  to  force  them  into  a 
given  course.  We  often  speak  of  events  happening  '  by  ' 
chance,  as  though  chance  were  a  real  cause.*  In  the  same 
way  when  we  speak  of  the  probabilities  as  favorable  or 
unfavorable  to  a  certain  event,  there  is  a  tendency  to  think 
of  these  shadowy  probabilities  as  allies  or  opponents  of  the 
event  in  question;  and  consequently  when  the  physician 
says  that  '  the  probabilities  are  slightly  favorable  '  we  feel 
more  like  rejoicing  than  when  he  merely  says  that  it  looks 
now  as  though  the  patient  might  recover.  The  conception 
of  probability  as  a  kind  of  inward  force  striving  to  work  itself 
out  is  called  by  Venn  "  one  of  the  last  remaining  relics  of 
[Scholastic]  Realism,  which  after  being  banished  elsewhere 
still  manages  to  linger  in  the  remote  province  of  Prob- 
ability." f 

*  Of  course  Chance  is  never  a  cause,  nor  does  the  word  imply  the  ab- 
sence of  causes.  "We  call  a  coincidence  casual,  I  apprehend,  when  we 
mean  to  imply  that  no  knowledge  of  one  of  the  two  elements,  which  we 
can  suppose  to  be  practically  attainable,  would  enable  us  to  expect  the 
other,  we  know  of  no  generalization  which  covers  them  both,  except  of 
course  such  as  are  taken  for  granted  to  be  inoperative.  In  such  an  ap- 
plication it  seems  that  the  word  'casual'  is  not  used  in  antithesis  to 
'  causal '  or  to  '  designed  ',  but  rather  to  that  broader  conception  of  order 
or  regularity  to  which  I  should  apply  the  term  Uniformity.  The  casual 
coincidence  is  one  which 'we  cannot  bring  under  any  special  generaliza- 
tion :  certain,  probable,  or  even  plausible  ".  (Venn,  24.6.) 

•j-  "  Logic  of  Chance  ",  p.  22. 


WHAT    IT    IS.  333 

Ho\v  then  shall  we  define  Probability  without  making  it 
either  a  measure  of  belief  or  a  mysterious  force  controlling 
things  ?  The  only  way  is  to  keep  the  objective 
standpoint  but  get  rid  of  the  mystery.  When 
we  say  that  the  probabilities  are  five  to  one  against  throwing 
six  with  a  single  die  in  any  one  throw,  the  only  clear  mean- 
ing we  can  have  is  this:  that  when  dice  are  thrown  a  large 
number  of  times  we  get  six  in  about  one-sixth  of  the  cases 
and  something  else  in  the  remaining  five-sixths.  Conse- 
quently before  we  make  the  throw  we  can  say  that  the 
probabilities  are  against  turning  up  a  six;  and  if  when  the 
throw  is  made  we  really  do  turn  up  a  six,  we  can  say  that  the 
improbable  has  occurred,  but  we  ought  not  to  say  that  our 
estimate  of  the  probabilities  had  been  erroneous,  even  though 
the  guess  we  based  upon  that  estimate  was  wrong.  The 
only  way  to  prove  that  the  estimate  of  the  probabilities  was 
erroneous  would  be  to  show,  either  by  direct  experiment  or 
from  the  nature  of  the  causes  involved,  that  in  the  long  run 
of  cases  essentially  similar  to  the  one  in  question  sixes  are 
not  turned  up  in  about  one  case  out  of  six.  In  the  same 
way,  when  we  say  that  a  man  of  thirty  will  probably  live  a 
year  longer,  all  we  mean  is  that  most  men  of  his  age  and 
apparent  health  do  live  a  year  longer.  We  do  not  mean  to 
say  that  this  particular  man  will  not  die  the  very  next  day. 
If  he  really  did  die  on  the  next  day,  we  could  say  once  more 
that  the  improbable  had  occurred  and  that  our  judgment  of 
the  probabilities  was  good  in  spite  of  the  event. 

The  statement  that  a  thing  may  be  improbable  and  yet 
occur  is  not  absurd.  When  we  throw  a  die  the  chances  are 
always  five  to  one  against  any  one  of  the  six  faces,  and  yet 
we  cannot  help  getting  one  of  them.  In  the  same  way  it 
is  highly  improbable  that  this,  that,  or  the  other  individual 
who  goes  into  a  lottery  will  win  the  prize;  and  yet  if  it  is  an 
honest  lottery,  one  of  them  must.  In  these  cases  the  improb- 
able has  to  occur.  Doubtless  it  is  often  said  that  if  an  event 
occurs,  that  very  fact  proves  that  it  was  not  really  improbable, 


334  PROBABILITY. 

and  that  if  it  does  not  occur,  that  proves  that  it  was  not 
really  probable,  although  it  may  very  well  have  seemed  so. 
Lut  when  people  speak  in  this  way  they  use  the  word 
'  Improbable  '  as  though  it  meant  '  Impossible  ',  and  the  word 
'  Probable  '  as  though  it  meant  '  Inevitable  '. 

Hence  all  that  we  mean  by  saying  that  a  certain  state  of 
affairs  is  probable  is  that  that  state  of  affairs  or  something 
which  is  bound  to  bring  it  about  actually  exists  in  most  cases 
of  the  sort.  It  does  not  mean  that  it  will  be  found  in  that 
individual  case.  The  outcome  in  the  individual  case  is 
unknown,  and  all  the  words  in  the  dictionary  will  not  turn 
ignorance  into  knowledge. 

But  if  the  '  probability  '  that  we  speak  of  with  reference  to 
a  particular  case  really  does  not  belong  to  that  particular 

case  at  all,  but  only  to  the  whole  series  or  class 
What  value?      ,  ....... 

of  cases  of  which  it  is  a  member,  what  good  does 

it  do  to  think  anything  about  it  when  the  question  at  issue 
is  not  concerned  with  the  series  or  class,  but  only  with  the 
individual  case  ?  It  may  be  very  interesting  to  know  that 
most  men  of  thirty  live  another  year;  but  what  good  does 
that  do  when  the  question  is  not  about  men  in  general,  but 
about  this  particular  man  ? 

None  whatever! — if  the  question  at  issue  really  does  con- 
cern this  individual  case  only.  If  a  person  is  going  to  do 
only  one  risky  thing  in  the  whole  course  of  his  life,  he  might 
as  well  do  it  with  his  eyes  shut  as  after  a  long  calculation  of 
probabilities.  Some  of  the  richest  strikes  in  the  world  have 
been  stumbled  upon  by  fools  and  tenderfeet  where  wise  men 
and  experts  have  missed  them.  It  is  a  pure  risk.  If  we  win 
we  win,  and  if  we  perish  we  perish,  and  in  the  latter  case  it 
will  not  be  much  consolation  to  be  assured  that  the  good 
fortune  we  missed  had  once  been  '  probable  '.  Generally, 
however,  the  question  is  not  of  one  case  only.  If  we  bet 
on  dice,  we  usually  mean  to  bet  more  than  once  and  we  are 
willing  to  lose  many  individual  bets,  provided  the  '  odds  ' 
are  so  arranged  that  we  win  at  least  as  much  as  we  lose  in 


WHAT   VALUE?  335 

the  long  run.  If  a  company  insures  lives  or  houses  or 
plate-glass  windows  at  all,  it  tries  to  insure  a  great  many  and 
it  expects  a  large  number  of  losses.  But  it  expects  still 
more  gains,  and  fixes  rates  that  will  make  the  total  gains  more 
than  meet  the  total  losses.  In  this  way  a  business  in  which 
every  single  operation  is  extremely  risky  becomes  on  the 
whole  one  of  the  very  safest  and  surest  that  a  person  can 
engage  in.  This  is  as  true  of  professional  gambling  as  it  is 
of  insurance — each  single  operation  is  as  risky  to  the 
'  banker'  as  it  is  to  the  chance  visitor;  but  if  he  only  bets 
often  enough  and  the  chances  are  slightly  in  his  favor,  his 
winnings  are  bound  to  be  greater  than  his  losses  in  the  long 
run.  Now  the  conditions  of  life  are  so  complex  that,  as  all 
the  proverbs  tell  us,  "  the  best  laid  schemes  o'  mice  and 
men  gang  aft  a-gley  ",  and  "nothing  is  certain  but  death 
and  taxes  ".  We  are  engaged  in  operations  which  are  more 
or  less  risky  all  our  lives  long.  Therefore  the  only  thing  to 
do  is  to  act  in  such  a  way  that  the  gains  will  more  than  make 
up  for  the  losses  in  the  long  run ;  that  is,  to  take  account  of 
the  relative  frequency  of  the  various  different  outcomes,  and 
where  odds — or  the  possible  gains  and  losses  in  a  single 
transaction — are  even  to  act  each  time  as  though  the  most 
frequent  outcome  were  going  to  be  present  then :  to  act 
'  on  general  principles'  or  '  according  to  the  probabilities  '. 
This  way  of  acting  on  general  principles  is  as  natural  as  it 
is  rational.  Nature  provided  for  it  when  she  made  us 
creatures  of  habit  and  imitation.  It  is  inculcated  in  every 
maxim  and  moral  rule.  And  because  it  is  so  natural  as  well 
as  so  rational  to  act  in  each  particular  case  with  reference 
to  the  general  principle  that  will  bring  us  out  right  in  the 
long  run,  we  come  to  feel  that  the  general  principle — whether 
it  be  a  principle  of  morals  or  of  probability — really  means 
something  for  the  individual  case  per  se;  and  consequently  it 
becomes  almost  impossible  to  get  far  enough  away  from  its 
influence  even  in  thought  to  realize  that  if  there  were  only 
one  uncertain  situation  in  the  whole  world  and  a  solitary 


33 6  PROBABILITY. 

human  being  who  had  to  venture  his  life  on  one  alternative 
or  the  other,  the  outcome  would  be  with  him  a  matter  of 
mere  unqualified  luck,  and  the  word  '  probability '  would 
have  absolutely  no  meaning. 

If  probability  belongs  to  an  individual  case  only  as  a 
member  of  a  class,  so  that  an  event  may  be  improbable  and 
still  occur,  why  is  it  that  the  estimation  of  probabilities  often 
wty  hard  seems  so  difficult,  and  what  is  the  difference 
to  estimate.  Between  good  judgment  in  estimating  them  and 
bad  judgment  ?  The  difficulty  which  makes  the  difference 
between  good  and  bad  judgment  so  apparent  is  nothing 
more  nor  less  than  the  difficulty  of  putting  each  individual 
case  into  the  best  class.  The  man  of  experience  in  any  par- 
ticular line  sees  distinctions  between  things  that  the  novice 
overlooks,  and  on  the  basis  of  these  distinctions  he  can  sub- 
divide his  classes  and  estimate  the  probabilities  in  any  par- 
ticular case  by  reference  to  the  subdivision  rather  than  to 
the  larger  class  to  which  the  case  belongs. 

A  stranger  to  the  United  States  who  happened  to  know 
that  the  two  great  political  parties  were  nearly  evenly  divided 
would  have  to  say  that  any  American  he  met  was  just  as 
likely  to  belong  to  the  one  as  to  the  other.  But  a  person 
who  knew  the  country  better  would  defer  his  judgment  until 
he  had  found  out  in  each  case  as  well  as  he  could  what  sec- 
tion of  the  country  the  person  in  question  came  from,  what 
race  he  belonged  to,  what  was  his  business,  and  so  on. 
Every  one  knows  that  there  is  some  danger  in  railroad  travel, 
and,  by  comparing  the  total  number  of  accidents  in  any 
given  country  during  a  given  year  with  the  total  number  of 
trains  run,  anybody  can  roughly  estimate  the  chances  of 
accident  on  some  particular  journey.  But  a  man  skilled  in 
such  matters  might  say  that  the  road  on  which  this  particular 
journey  was  to  be  taken  had  a  double  track  and  block  sig- 
nals and  tests  for  color-blindness  and  this  particular  kind  of 
brake  and  that  particular  kind  of  coupler,  and  that  where 
they  had  all  these  things  the  proportion  of  accidents  to  trains 


CAUTION.  337 

— i.e. ,  the  '  chance'  of  accident — was  very  much  less  than 
in  the  country  at  large.  If  he  happened  to  know  the  records 
of  the  men  who  had  charge  of  that  particular  train,  he  might 
form  a  more  accurate  estimate  still.  In  the  same  way,  a 
physician  examining  an  applicant  for  life  insurance  does  not 
think  of  him  merely  as  a  person  of  a  given  sex  and  age  who 
looks  strong  or  delicate.  He  regards  him  as  a  person  with 
a  certain  heredity,  certain  habits,  certain  lung  capacity  and 
heart  action,  and  with  or  without  symptoms  of  this,  that, 
and  the  other  definite  disease. 

Such  details  do  not  tell  how  any  given  case  will  turn  out; 
but  they  enable  one  to  classify  it  with  a  small  group  of  cases 
that  resemble  it  quite  closely  rather  than  with  a  larger  group 
that  resemble  it  rather  vaguely;  and  if  the  proportion  of 
cases  in  which  an  event  (such  as  a  railroad  accident)  occurs 
or  (if  it  is  an  event  like  death  that  must  occur  in  every  case) 
the  average  interval  before  its  occurrence  is  something  which 
we  know  as  accurately  for  the  smaller  group  as  for  the 
larger,  this  is  a  distinct  advantage;  for  the  greater  the 
resemblance  between  all  the  individuals  in  a  group  the 
smaller  is  the  variation  between  the  outcome  for  any  partic- 
ular case  and  the  average  outcome  for  the  class.  If  we  could 
find  a  past  case  that  we  knew  to  be  absolutely  similar  to  the 
one  in  question  in  every  particular,  and  could  thus  base  our 
judgment  upon  what  we  knew  about  a  class  of  one,  proba- 
bility would  come  to  an  end  and  we  should  have  certainty. 
The  greater  our  knowledge  and  skill  the  nearer  can  we  come 
to  such  a  class.  Hence  it  is  in  the  subdivision  of  classes 
and  the  knowledge  of  the  outcome  for  each  that  the  difficulty 
and  the  room  for  special  skill  come  in. 

If  probability  is  not  a  force  and  therefore  exerts  no  influ- 
ence on  the  course  of  events,  it  is  a  mistake  to  believe  that 

the  non-occurrence  of  a  probable  event  at  one 

...     .  Caution. 

time    makes    it    any   more    likely   to    occur   at 

another.  If  a  person  is  tossing  a  coin  and  gets  heads  three 
times  running,  he  is  likely  to  say  that  next  time  it  must  be 


338  PROBABILITY. 

tails.  But  this  is  a  blunder.  It  is  conceivable  that  one  toss 
of  a  coin  will  affect  another,  just  as  a  man's  success  in  one 
enterprise  may  give  him  the  confidence  that  leads  to  success 
or  the  overconfidence  that  leads  to  failure  in  the  next.  But 
if  there  is  no  such  causal  relation  as  this  between  the  events 
themselves,  probability  is  not  going  to  become  a  cause  and 
make  one  toss  balance  another.  Whether  we  have  tossed 
heads  three  times  running  or  ten  times,  the  coin  will  know 
nothing  about  it  and  the  result  of  the  next  throw  will  be 
exactly  what  it  would  have  been  if  no  throws  had  preceded 
it  at  all.  In  the  same  way  if  a  very  improbable  event  occurs 
at  one  moment,  that  is  no  reason  for  believing  that  it  will  not 
occur  again  at  the  very  next.  Lightning  is  quite  as  likely 
to  strike  again  in  the  same  place  (the  proverb  to  the  contrary 
notwithstanding)  as  to  strike  in  any  other  given  place  of  the 
same  size.  A  second  Galveston  disaster  is  quite  as  likely  to 
come  exactly  ten  years  after  the  first  as  to  come  exactly  137 
years  and  48  days  after.  We  are  quite  as  likely  to  throw 
ten  heads  running  as  nine  heads  and  then  one  tail,  or  any 
other  precisely  designated  series.* 

The  reductio  ad  absurdum  of  this  view  that  events  must 
balance  and  come  out  according  to  the  probabilities  is  found 
in  the  story  of  the  physician  who  said  to  his  patient: 
'  Madam,  you  can't  help  getting  well;  for  the  books  say  that 
one  case  out  of  every  hundred  does,  and  I  have  already  lost 
ninety-nine.' 

The  mathematical   calculation  of  probabilities  is  in  the 

main  very  simple — so  far  at  least  as  the  underlying  principle/ 

are  concerned.     If  we  are  tossing  a  single  die,  Wv 

matical  expect  to  turn  up  one  face  in  the  long  run  about 

as  often  as  any  other,  or,  in  other  words,  to  turn 

up  any  given  face  in  one-sixth  of  the  total  number  of  throws. 

*  Of  course  a  series  is  not  precisely  designated  unless  the  order  of  the 
heads  and  tails  is  designated  as  well  as  their  total  number.  •  Nine  heads 
and  then  one  tail '  does  not  mean  the  same  thing  as  '  nine  heads  and  one 
tail ',  for  this  last  does  not  tell  which  one  of  all  the  ten  throws  the  tail  is 
to  be. 


MATHEMATICAL   PRINCIPLES.  339 

We  therefore  say  that  the  chance  of  getting  that  face — say 
the  six — is  |.  Since  the  ace  and  the  six  each  occur  in  one- 
sixth  of  the  total  number  of  throws,  one  or  other  of  them  will 
occur  in  one-third  of  the  total  number;  and  so  we  say  that 
the  chance  of  getting  either  an  ace  or  a  six  i.s  \,  and  so  on. 
It  will  be  noticed  in  this  case  that  the  throw  which  gives  any 
one  of  the  six  faces  cannot  by  any  possibility  give  any  other; 
and  so  we  can  make  some  such  general  statement  as  this: 
Where  two  or  more  events  are  incompatible  the  chance  of 
getting  either  one  or  the  other  is  found  by  adding  together 
the  fractions  which  express  the  chances  of  each.  Of  course 
the  chances  against  any  given  event  or  alternative  are  found 
by  subtracting  the  fraction  in  favor  of  it  from  i. 

When  we  are  tossing  t\\o  dice  (A  and  13)  instead  of  one, 
we  expect  that  in  the  long  run  each  of  the  following  com- 
binations will  occur  about  as  often  as  any  other: 


A 

B 

A 

B 

A 

B 

A 

B 

A 

B 

A 

B 

i 

i 

2 

i 

3 

i 

4 

i 

5 

i 

6 

I 

i 

2 

2 

2 

3 

2 

4 

2 

5 

2 

6 

2 

i 

3 

2 

3 

3 

3 

4 

3 

5 

3 

6 

3 

i 

4 

2 

4 

3 

4 

4 

4 

5 

4 

6 

4 

i 

5 

2 

5 

3 

5 

4 

5 

5 

5 

6 

5 

i 

6 

2 

6 

3 

6 

4 

6 

5 

6 

6 

6 

With  reference  to  the  6   or  any  other  given  face  we  can 
summarize  these  results  as  follows: 

A  six  and  B  six,  i  X  -^  times  =  -^ 

A  six  and  B  not  six,  i  v  A     " 


3  « 
5 

3TT 

A  not  six  and  B  not  six,   I-  X 


A  not  six  and  B  six, 


6    -^    C  ~    3  6 

Total |f~ 

Putting  these  results  into   more  general  form:    "If  the 

chances  of  a  thing  being  p  and  a  are  respectively  —  and  -, 

m  n 

then  the  chance  of  its  being  both  p  and  q  is  — ,  p  and  not 

mn 


340  PROBABILITY. 

n  —  i  m  —  i 

q   is ,   a  and    not   p   is    — ,   not  *  and   not    q   is 

run  mn    ' 

(m  -•  i)(«  —  i)  „, 

— -'    where  p  and  q  are  independent.      1  he  sum 
mn 

of  these  chances  is  obviously  unity;  as  it  ought  to  be,  since 
one  or  other  of  the  four  alternatives  must  necessarily 
exist. "  * 

One  thing  that  a  non-mathematician  is  liable  to  overlook 
in  these  figures  is  this,  that  the  throws  in  which  we  get  a  six 
with  either  of  two  dice  are  not  so  common  as  the  throws  in 
Four  more  which  we  get  either  a  six  or  an  ace  with  one 
cautions.  jje_  vye  tum  Up  as  manv  sjxes  wjth  the  two 

dice  as  we  turn  up  sixes  and  aces  with  one;  but  since  the 
two  sixes  are  on  different  dice  and  are  therefore  not  in- 
corrpatible,  they  come  together  in  one  throw  out  of  thirty- 
six,  and  we  do  not  turn  them  up  in  so  many  separate  throws. 
This  explains  the  necessity  for  the  word  '  incompatible  '  in 
the  formula  which  we  gave  on  page  339. 

A  second  thing  to  notice  about  the  table  has  been  already 
referred  to  in  another  connection:  namely,  that  if  we  add 
together  the  numbers  on  the  two  dice  in  each  throw,  we  shall 
find  that  one  sum  is  by  no  means  as  common  as  another. 
Seven  is  the  commonest,  for  it  can  be  made  by  six  different 
combinations;  6  and  8  next;  then  5  and  9,  and  so  on  until 
we  reach  2  and  12,  each  of  which  occurs  only  once.  Thus 
once  more  the  mean  is  commoner  than  the  extremes. 

A  third  thing  about  these  tables  is  worth  dwelling  upon 
because  we  are  all  likely  to  forget  it  when  the  figures  are  not 
before  us:  namely,  the  extremely  small  number  of  cases  in 
which  two  independent  improbable  events  coincide.  Sixes 
with  a  single  die  are  thrown  in  one  case  out  of  six,  but 
double  sixes  with  two  dice  in  only  one  out  of  thirty-six,  and 
if  we  should  guess  double  sixes  as  often  as  they  are  thrown 
(i.e.,  one  time  out  of  thirty-six)  the  guess  would  be  right 

*  Venn,  p.  174. 


FOUR   MORE   CAUTIONS.  341 

(i.e.,  coincide  with  the  throw)  in  only  one  case  out  of 
36  X  36,  i.e.,  in  one  out  of  1296.  To  take  another  example 
of  the  same  thing,  if  the  chances  of  taking  a  certain  disease 
are  y-J-^,  and  if  a  first  attack  neither  increases  nor  decreases 
the  liability  to  a  second,  the  chance  of  a  given  person  having 
that  disease  twice  is  only  yoioir  ^n  otner  words,  if  one 
person  out  of  100  has  it  once,  only  one  out  of  10,000  will 
have  it  twice.  The  difference  between  these  two  figures  is 
of  course  very  striking,  and  any  one  who  sees  them  is  likely 
to  forget  about  the  mathematics  and  jump  to  the  conclusion 
that  a  first  attack  affords  almost  complete  immunity  against 
a  second.  As  Wallace  says  in  his  very  ingenious  (though 
by  no  means  conclusive)  article  against  Vaccination  :  "  '  Very 
few  people  have  smallpox  a  second  time.'  No  doubt. 
But  very  few  people  suffer  from  any  special  accident  twice — 
a  shipwreck,  or  railway  or  coach  accident,  or  a  house  on 
fire;  yet  one  of  these  accidents  does  not  confer  immunity 
against  its  happening  a  second  time.  The  taking  it  for 
granted  that  second  attacks  of  smallpox,  or  of  any  other 
zymotic  disease,  are  of  that  degree  of  rarity  as  to  prove  some 
immunity  or  protection,  indicates  the  incapacity  of  the 
medical  mind  for  dealing  with  what  is  a  purely  statistical 
and  mathematical  question.  "  *  Unfortunately  "  the  medical 
mind  "  is  not  the  only  one  that  is  likely  to  forget  how 
rapidly  fractions  diminish  when  they  arc  squared. 

The  method  of  ascertaining  causal  relations  by  comparing 
the  number  of  actual  coincidences  between  two  events  or 
circumstances  with  the  number  that  would  naturally  be  pro- 
duced by  mere  chance  according  to  the  theory  of  probability 
is  being  used  more  and  more  as  statistics  of  various  sorts 
become  more  and  more  available;  and  by  this  method  we 
must  expect  to  reach  many  conclusions  that  seem  at  first,  for 
the  reason  just  given,  to  be  contrary  to  all  experience. 

A   fourth   word   of   warning   about    the   interpretation    of 


*  Alfred  R.  Wallace,    "  The  Wonderful  Century  ",  N.  Y., 


342 


PROBABILITY. 


tables  of  probability.  That  an  event  turns  out  so  many 
times  in  a  given  way  is  no  reason  why  we  should  act  that 
many  times  as  though  we  expected  it  to  turn  out  that  way. 
On  the  contrary  we  should  act  each  time  as  though  we 
expected  it  to  turn  out  in  the  most  probable  way.  If  we  are 
guessing  the  total  number  of  spots  turned  up  by  two  dice 
and  if  we  guess  7  every  time,  we  will  be  right  in  6  cases  out 
of  36,  or  216  out  of  1296.  But  if  we  should  guess  each 
number  as  many  times  as  that  number  is  actually  turned  up, 
we  should  be  right  in  only  146  cases  out  of  1296,  as  the 
following  table  shows  : 


Number. 


3 

4 

5 
6 

7 

8 

9 

10 
ii 


12 


Times 

Times 

Times  guessed 

thrown 

guessed 

right  out  of  36' 

out  of  36 

out  of  36 

or  1296  total 

throws. 

guesses. 

guesses. 

I 

I 

I 

2 

2 

4 

3 

3 

9 

4 

4 

16 

5 

5 

25 

6 

6 

36 

5 

5 

25 

4 

4 

16 

3 

3 

9 

2 

2 

4 

I 

I 

i 

Total  number  of  correct  guesses  146. 


AVhat  is  true  in  this  case  is  true  in  any  other:  we  should 
act  each  time  as  though  we  expected  the  most  probable  out- 
come to  be  found  then.  The  figures  show  how  much  we 
can  afford  in  the  long  run  to  risk  upon  each  guess.  They 
do  not  show  how  many  times  in  the  long  run  each  of  the 
possible  outcomes  should  be  guessed. 


CHAPTER  XXXIII. 

OBSERVATION  AND  MEMORY. 

INDUCTION  tries  to  weave  facts  together  into  a  coherent 
world.  But  our  knowledge  of  every  one  of  these  facts  de- 
pends sooner  or  later  upon  a  perception  through  the  senses  ; 
and  if  our  '  senses  deceive  us  '  and  we  perceive  or  think 
we  perceive  what  is  not  really  present,  that  false  perception 
will  tend  to  give  us  a  wrong  conception  of  the  world.  Hence 
it  is  necessary  to  know  something  about  the  difference  be- 
tween good  and  bad  perceptions.  Moreover  many  of  the 
perceptions  from  which  we  draw  inferences  took  place  some 
time  ago,  and  if  we  depend  upon  our  memory  but  do  not 
remember  them  correctly,  we  areas  badly  off  as  if  the  percep- 
tions themselves  were  wrong.  Hence  we  must  consider 
memory  also. 

The  first  thing  to  learn  about  Observation  is  the  vast  dif- 
ference between  what  one  actually  perceives  and  the  inference 

bv    which  he   explains  it.      The  word   '  Observa- 

,  -  ...          Observation 

tion     seems  to  refer  to  the  perception  only  ;   but   and  infer- 
as  it  is  generally  used  it  includes  a  vast  amount  of 
inference   also.      To  explain  this  difference.      A  Frenchman 
makes  a  flying  visit  to  the  United  States  and  then  goes  home 
to  write  a  book   in  which  he  recounts  his  observations  upon 
the  character  of  the  American  people.    But  the  '  observations  ' 
he  recounts  involve  at  least   three   successive  sets  of  infer- 
ences.    What  he  has  really  observed  is  a  specific  set  of  words 
and  acts  on  the  part  of  this,  that,  and  the  other  specific  indi- 

343 


344  OBSERVATION   AND   MEMORY. 

vidual.  His  first  inference  is  that  by  these  words  the  indi- 
viduals in  question  intended  to  convey  certain  specific  ideas, 
and  that  in  the  acts  they  were  guided  by  certain  specific  pur- 
poses; but  he  may  have  wholly  misunderstood  them  both.  His 
second  inference  is  that  people  wishing  to  convey  such  ideas  or 
acting  for  such  purposes  must  have  such  and  such  character- 
istic conceptions  and  feelings  ;  but  again  he  may  be  mistaken. 
His  third  inference  is  that  what  is  characteristic  of  this  score 
or  more  of  individuals  whom  he  happens  to  have  met  is  char- 
acteristic also  of  the  seventy-six  millions  whom  he  has  not. 
Once  more  he  may  be  wrong.  Yet  he  calls  it  all  observation. 

So  with  scientists.  Their  inferences  are  more  careful;  but 
still  they  often  use  the  word  Observation  to  include  them. 
Astronomers,  for  example,  may  speak  of  the  observed  course 
of  such  and  such  a  comet,  when  they  have  only  observed  a 
few  of  its  positions  and  have  calculated  all  the  rest.  Indeed 
in  the  strictest  sense  of  the  word  they  can  hardly  be  said  to 
have  observed  even  a  single  position.  They  have  perceived 
a  speck  of  light  at  a  certain  apparent  position  in  the  field  of 
a  telescope;  at  about  the  same  time  they  pressed  an  electric 
key  connected  with  a  clock  ;  and  they  have  afterwards  read 
off  certain  figures  from  various  parts  of  the  telescope  and  its 
attachments.  That  is  all.  The  position  of  the  comet  even 
at  one  moment  is  obtained  from  these  data  and  others  like 
them  by  elaborate  calculations.  Thus  the  word  'observation' 
is  used  in  science  as  well  as  in  common  life  in  a  very  loose 
sense  that  is  likely  to  deceive  because  it  seems  to  imply  a 
closer  contact  with  immediate  experience  than  it  really  does. 

Even  when  we  reali/e  all  this  and  do  not  regard  anything 
as  an  Observation  except  a  direct  perception  we  are  not  yet 
free  from  inference.  Perceptions  are  not  bare  sensations. 
They  are  sensations  interpreted,  and  the  interpretation,  how- 
ever rapid  and  involuntary,  is  an  inference,  and  may  be 
wrong.  I  see  my  brother  across  the  road,  but  when  I  cross 
to  speak  to  him  it  turns  out  to  be  some  one  else  ;  I  hear  some 
one  say  '  Be  honorable  ',  but  he  really  said  '  It's  in  an  enve- 


CREDULITY.  345 

lope  ',  and  so  on.  These  are  what  psychologists  call  Illusions. 
Then  again  we  have  Hallucinations,  when  the  interpreted 
sensation  itself  arises  wholly  from  within.  I  hear  my  name 
called,  see  a  flash  of  light,  or  feel  a  drop  of  rain  or  the  crawl- 
ing of  ants,  when  there  is  nothing  there  at  all.  But  because 
I  say  '  There  is  '  a  sound,  a  light,  or  an  insect,  instead  of 
merely  saying  '  I  have  '  such  and  such  a  feeling,  or  that  such 
and  such  a  feeling  exists,  I  am  drawing  an  inference  once 
more,  and  once  more  it  is  or  may  be  wrong.  The  only  way 
to  avoid  all  chance  of  Illusions  and  Hallucinations  is  not  to 
interpret  any  sensation.  But  a  live  person  cannot  do  this ; 
and  if  he  could  and  did,  he  would  die. 

Thus  the  paradox  :  induction  sets  out  to  base  its  inferences 
upon  the  observation  of  facts,  but  the  observation  is  itself  a 
matter  of  inference.  What  then  shall  we  do  :  reduce  the 
element  of  inference  in  our  observations  to  the  very  minimum 
mentally  possible,  or  let  it  reach  a  maximum  ?  What  we 
really  do  in  most  cases  is  to  infer  without  scruple  until  some- 
thing makes  us  suspect  that  we  have  been  deceived  or  that 
we  are  dealing  with  a  class  of  facts  in  which  we  are  likely  to 
be  deceived;  and  then,  if  it  is  not  too  late,  we  turn  back  and 
examine  the  phenomena  more  carefully  and  critically.  No 
one  ever  thinks  of  distrusting  his  '  senses  '  so  much  when  he 
is  watching  a  farmer  or  a  carpenter  at  work  as  when  he  is 
watching  a.  conjurer  or  a  'medium'.  In  the  one  case  we 
include  a  great  many  spontaneous  inferences  in  our  '  ob- 
servations '  and  say  that  we  saw  him  do  thus  and  so  ;  in  the 
other  case  we  only  say  that  he  seemed  to.  What  we  do  natu- 
rally in  this  respect  is  perfectly  logical;  for  no  apparent  per- 
ception can  be  tested  except  by  the  surrounding  conditions 
as  we  know  them. 

All  the  difference  between  the  absurd  credulity  or  incredu- 
lity of  ignorant  peasants  and  the  reasonable  judgment  of  the 

educated   depends  upon   the  different   extent  of 

Credulity. 
their  knowledge  about  phenomena  like  those  in 

question  or  the  wider  world  in  which  they  occur.     A  scientist 


346  OBSERVATION    AND   MEMORY. 

never  thinks  of  doubting  the  existence  of  other  men,  and 
thus  when  he  'sees'  a  colleague  in  the  room  with  him 
he  believes  that  the  colleague  is  there.  An  unsophisticated 
peasant  never  thinks  of  doubting  the  existence  of  ghosts,  and 
so  when  he  '  sees '  a  ghost  in  the  room  with  him  he  believes 
that  it  is  there.  Logically  the  scientist  and  the  peasant  are 
in  precisely  the  same  position,  and  unless  we  are  willing  to 
say  that  the  scientist  should  not  be  so  credulous  when  he 
believes  that  he  sees  something,  we  have  no  right  to  say  it  of 
the  peasant.  Incredulity  in  general  is  no  better  than  credu- 
lity. The  scientist  would  probably  distrust  his  '  observa- 
tion' of  the  ghost,  but  he  does  not  distrust  his  observation  in 
general.  Indeed  he  distrusts  his  'observation'  of  the  ghost 
only  because  he  trusts  his  other  observations  and  the  infer- 
ences he  has  drawn  from  them  enough  to  believe  that  ghosts 
probably  do  not  exist.  Thus  in  observation,  as  in  every- 
thing else,  general  faith  precedes  and  has  a  logical  right  to 
precede  specific  doubt.  The  doubt  does  not  come  sponta- 
neously or  for  its  own  sake,  but  it  is  forced  upon  us  by  our 
faith  in  our  other  observations  and  the  larger  system  of 
things  which  they  seem  to  have  revealed. 

If  the  field  of  our  observations  is  a  new  one  and  we  cannot 
tell  where  it  is  that  the  spontaneous  inferences  which  we 
naturally  include  in  our  'observations'  are  most  likely  to  be 
wrong,  the  only  thing  to  do  is  to  go  ahead  bravely  yet 
cautiously,  placing  provisional  confidence  in  our  observations 
everywhere,  yet  always  ready  to  turn  back  and  re-examine 
any  point  more  carefully.  The  scientist  cannot  avoid  blun- 
ders ;  for  he  sees  and  hears  as  other  men  do,  and  he  draws 
all  their  spontaneous  inferences  ;  but  unlike  them  he  knows 
ho\v  much  of  what  he  seems  to  see  and  hear  is  really  infer- 
ence, and  how  likely  it  therefore  is  that  some  of  his  'obser- 
vations' are  erroneous.  Consequently  he  generally  takes 
pains  to  verify  his  observations  before  he  announces  them, 
he  states  them  modestly  when  he  docs,  he  expects  others  to 
verify  them  for  themselves  before  accepting  them,  and  he  is 


UNPREJUDICED    OBSERVERS.  347 

willing  to  be  corrected  when  he  has  made  a  mistake.  In  all 
of  which  respects  he  is  very  different  from  most  of  those  who 
have  not  received  his  training. 

Since  what  we  '  observe  '  and  the  faith  we  put  in  it  depend 
upon  what  we  already  believe,  it  is  perfectly  evident  that 
a  wrong  belief  to  begin  with  will  lead  to  wrong 

'  observations '    so  that  when  we  are  once  started   Errors 

cumulative. 

on   the  wrong  track  we  keep  going  further  and 

further,  and  generally  find  '  sufficient  proofs  '    for  our  false 

convictions. 

Trifles  light  as  air 

Are  to  the  jealous  confirmations  strong 
As  proofs  of  holy  writ. 

We  pile  proof  upon  proof  until  at  last  we  stumble  across 
some  fact  so  obvious  that  we  cannot  ignore  or  distort  it,  or 
until  we  discover  that  the  general  conception  of  things  that 
led  to  so  many  bad  'observations'  is  inconsistent  with  some 
other  general  conception  just  as  well  'established'.  Then 
comes  the  doubt,  the  true  testing  of  the  'observations',  and 
the  belter  general  standpoint.  The  only  point  in  favor  of 
the  scientist  as  contrasted  with  other  people  is  that  he  is  on 
the  watch  for  such  inconsistencies,  and  therefore  corrects  his 
blunders  of  theory  and  observation  sooner. 

This  danger  of  '  observing '  what  we  expect  to  observe 
and  ignoring  what  we  do  not  is  inevitable.  Often  we  wi>h 
to  submit  a  fact  to  an  unprejudiced  observer.  If  we  mean  by 
an  'unprejudiced'  observer  one  who  has  abso- 
lutely no  convictions  that  can  possibly  affect  his 
observations,  then  the  only  unprejudiced  ob- 
servers in  the  world  are  newly  bom  babies  who  do  not  even 
believe  that  there-  are  things  and  people.  But  their  freedom 
from  prejudice  makes  it  impossible  for  them  to  '  observe  ' 
anything  at  all.  When  we  demand  the  testimony  of  an  'un- 
prejudiced observer '  the  most  that  we  can  really  wish  is  that 
the  observer  in  question  shall  have  no  more  personal  interest 
in  one  side  of  the  question  at  issue  than  in  the  ether,  that  he 


OBSERVATION   AND   MEMORY. 

shall  have  conceived  of  both  sides  as  distinctly  as  possible, 
and  that  he  shall  then  have  made  his  observations  dispas- 
sionately, calmly,  and  deliberately  for  the  sake  of  deciding 
as  fairly  as  possible  between  the  two  sides.  We  do  not  ask 
that  his  mind  shall  be  free  from  all  preliminary  convictions, 
but  only  from  those  special  convictions  the  truth  of  which  is 
disputed  by  one  side  or  the  other.  He  is  not,  and  cannot 
be,  without  prejudice  in  general,  but  only  without  prejudice 
on  the  questions  involved  in  this  particular  dispute.  For  the 
rest,  we  must  expect  him  to  take  something  for  granted. 
Hence  if  the  question  changes  after  the  observations  are 
made  and  now  the  dispute  turns  upon  some  point  that  our 
unprejudiced  witness  never  seriously  questioned,  his  testi- 
mony is  no  longer  of  any  special  value.  And  so,  in  general, 
an  observation  made  for  the  sake  of  settling  one  question  has 
very  little  value  for  the  settling  of  another.  When  the  ques- 
tion is  changed  the  observations  should  be  repeated. 

Errors  of  observation  are  divided  by  logicians  into  those 
of  Mai-Observation,  where  we  perceive  things  wrongly,  as 
Two  classes  has  just  been  explained,  and  those  of  Xon-Obser- 
of  errors.  vation,  where  we  fail  to  perceive  or  take  account 
of  certain  important  facts  at  all.  Here  are  some  examples 
of  the  latter. 

"Most  of  the  books  do  not  give  us  a  psychology,  but 
rather  a  eulogv,  of  animals.  They  have  all  been  about  ani- 
mal intelligence,  never  about  animal  stupidity.  .  .  .  Human 
folk  are  as  a  matter  of  fact  eager  to  find  intelligence  in  ani- 
mals. They  like  to.  And  when  the  animal  observed  is  a 
pet  belonging  to  them  or  to  their  friends,  or  when  the  story 
is  one  that  has  been  told  as  a  story  to  entertain,  further  com- 
plications are  introduced.  Nor  is  this  all.  Besides  com- 
monly misstating  what  facts  they  report,  they  report  only 
such  facts  as  show  the  animal  at  his  best.  Dogs  get  lost 
hundreds  of  times  and  no  one  ever  notices  it  or  sends  an 
account  of  it  to  a  scientific  magazine.  But  let  one  find  his 
way  from  Brooklyn  to  Yonkers  and  the  fact  immediately 


TWO   CLASSES   OF   ERRORS.  349 

becomes  a  circulating  anecdote.  Thousands  of  cats  on  thou- 
sands of  occasions  sit  helplessly  yowling,  and  no  one  takes 
thought  of  it  or  writes  to  his  friend,  the  professor;  but  let 
one  cat  claw  at  the  knob  of  a  door,  supposedly  as  a  signal  to 
be  let  out,  and  straightway  this  cat  becomes  the  representa- 
tive of  the  cat-mind  in  all  the  books.  The  unconscious  dis- 
tortion of  the  facts  is  almost  harmless  compared  to  the  un- 
conscious neglect  of  an  animal's  mental  life  until  it  verges  on 
the  unusual  and  marvellous. ' '  * 

Again,  during  a  thunder-storm  a  timid  woman  often  tries  to 
justify  her  fears  by  recounting  all  the  cases  she  can  remember 
of  persons  who  were  struck  or  nearly  struck  by  lightning  in 
previous  storms,  and  forgets  the  thousands  who  lived  through 
them  unscathed.  Many  a  man  buys  a  ticket  for  a  lottery 
because  he  thinks  his  '  chances  ought  to  be  as  good  '  as  those 
of  some  acquaintance  who  once  won  a  prize,  but  forgets  that 
they  are  also  as  bad  as  those  of  unnamed  hundreds  who  in- 
vested but  never  won.  "  Bacon  quotes  the  case  of  the  scep- 
tic in  the  temple  of  Poseidon,  who,  when  shown  the  offerings 
of  those  who  had  made  vows  in  danger  and  been  delivered, 
and  a>ked  whether  he  did  not  now  acknowledge  the  power  of 
the  god,  replied  :  '  But  where  are  they  who  made  vows  and 
yet  perished  '  ?  This  man  answered  rightly,  says  Bacon.  In 
dreams,  omens,  retributions,  and  such  like,  we  are  apt  to 
remember  when  they  come  true  and  to  forget  the  cases  when 
they  fail.' '  f 

Errors  of  observation  are  sometimes  spoken  of  as  Fallacies. 
This  does  not  mean  that  it  is  a  fallacy  not  to  see  something 
that  is  there.  The  fallacy  comes  in  when  we  infer  that  it  was 
not  there  because  we  did  not  see  it.  I  may  not  notice  the 
number  of  times  that  dreams  fail  to  come  true,  but  I  commit 
no  fallacy  unless  this  makes  me  infer  that  they  come  true 
much  oftener  in  proportion  than  they  really  do.  In  the  same 
way  it  would  be  rather  a  straining  of  language  to  call  an 

*  E.  L.  Thorndike,  "Animal  Intelligence",  pp.  3-5.     Macmillan. 
•j-  Minto's  "Logic",  p.  24. 


35°  OBSERVATION   AND   MEMORY. 

erroneous  observation  a  fallacy.  The  fallacy  or  blunder  in 
reasoning  comes  in  when  we  do  not  make  proper  allowance 
for  the  possibility  of  such  errors,  and  insist  that  something 
must  be  true  because  '  we  saw  it ' . 

When  an  observation  is  not  fully  recorded  at  the  time  of 
making,  the  danger  of  error  is  twofold;  for  we  are  quite  as 
likely  to  be  wrong  in  our  memory  of  the  observa- 
its™ange«d  tion  as  in  the  observation  itself.  The  longer  the 
time  between  the  observation  and  the  recollection 
the  greater  in  general  is  the  danger  of  error.  "  Col.  Nicolay 
is  reported  to  have  said  that  he  and  Mr.  Hay  received  very 
little  aid  from  contemporary  memories  in  writing  their  his- 
tory of  Abraham  Lincoln,  and  that  they  came  to  the  con- 
clusion that  mere  memory  unassisted  by  documentary  evidence 
was  'utterly  unreliable  after  a  lapse  of  fifteen  years  '."  * 

The  dangers  in  the  case  of  Memory  are  like  those  in  the 
case  of  observation.  We  may  forget,  and  if  we  insist  un- 
reasonably that  we  never  had  a  certain  experience  because 
we  cannot  remember  it,  we  commit  precisely  the  same  kind  of 
blunder  as  when  we  insist  unduly  that  a  thing  was  not  present 
because  we  did  not  observe  it. 

When  we  do  '  remember  '  we  are  more  likely  than  not  to 
get  some  of  the  details  wrong,  and  sometimes  we  take  '  recol- 
lections '  for  true  when  they  are  really  complete  inventions. 
Errors  of  the  first  kind  correspond  to  illusions  in  perception; 
those  of  the  second  kind  to  hallucinations. 

In  memory  as  in  perception  we  constantly  tend  to  find 
what  we  think  we  ought  to  find.  When  we  tell  a  story  of 
some  past  conduct  of  our  own  we  almost  inevitably 
'Member  niake  it  more  logical  and  coherent  than  it  really 
was.  We  had  the  motives  that  we  ought  to  have 
had,  we  said  the  clever  things  that  we  ought  to  have  said, 
and  the  mere  blind  impulses  and  incoherent  acts  and  mean- 
ingless speeches  are  forgotten  altogether  or  twisted  into 

*  W.  II.  Burnham,   "Memory",  Am.  Jour,  of  Psychology,  II.  235. 


WHAT   WE   REMEMBER.  351 

shape.*  When  things  are  simply  incoherent  and  meaningless 
we  cannot  remember  them,  any  more  than  we  can  observe 
them.  We  may  remember  that  there  was  something  incoher- 
ent, but  we  cannot  remember  or  describe  it  without  giving  it 
a  certain  coherence,  even  if  it  be  a  coherence  of  absurdity. 
When  someone  makes  a  meaningless  speech  \ve  either  give  it 
a  reasonable  meaning,  forget  it  altogether,  or  make  it  a  kind 
of  monstrosity  far  worse  than  it  really  was.  If  it  does  not 
make  a  definite  impression  of  some  kind  or  other,  we  forget  it. 
If  it  does,  we  fill  in  all  the  details  to  fit  our  notion  of  the  whole. 
It  is  the  same  way  in  our  recollection  of  an  argument  or  a 
quarrel.  We  were  right  and  our  opponent  was  wrong  ;  and 
we  remember  our  good  sayings  or  acts  and  his  bad  ones 
because  they  fit  in  with  the  impression  of  our  Tightness, 
and  forget  our  bad  sayings  or  acts  and  his  good  ones  because 
they  do  not  fit  in  with  this  impression  and  are  therefore  in  a 
sense  purely  irrelevant.  Or  it  may  be  that  we  are  impressed 
with  the  wrongness  of  our  case,  and  then  we  go  to  the  other 
extreme  and  remember  our  own  bad  sayings  and  acts  and  his 
good  ones  and  forget  our  cwn  good  and  his  bad.  In  either 

*  "Mere  illusions  of  memory  suggested  by  present  impressions  are 
common  in  normal  life.  As  we  apperceive  any  object  or  event  through 
the  media  of  the  feelings  and  ideas  in  consciousness  at  the  moment,  and 
thus  no  two  of  us  apperceive  the  same  tiling  in  the  same  \v,iy.  so  in  rec- 
ollection each  apperceives  the  past  from  the  standpoint  of  his  present 
state  of  consciousness,  and  the  latter  bears  its  part  in  determining  what 
the  resulting  recollections  shall  be.  We  remember  only  main  features 
of  an  event  anyway,  and  the  imagination  fills  in  the  gaps.  Thus  re- 
membrance is  never  a  true  reproduction  of  reality.  Tt  is  always  more 
or  less  an  illusion.  At  best  it  is  an  approximation  to  the  truth.  How 
near  an  approximation  depends  largely  upon  the  apperceptive  mood  of 
the  moment."  (W.  H.  Burnham,  "Memory",  Am.  J.mr.  of  Psychol- 
ogy, II,  449-5°-) 

Consistency  according  to  the  laws  of  nature  is  the  only  test  of  truth  ; 
but  consistency  in  conduct  is  consistency  according  to  a  purpose,  and 
this  is  only  an  ideal.  When  a  person  tells  a  story  that  makes  all  his 
acts  or  all  the  acts  of  his  hero  rat'onal  and  consistent,  we  can  be  quite 
sure  that  it  is  not  true. 


35 2  OBSERVATION   AND   MEMORY. 

case  the  recollection  is  distorted  by  the  almost  inevitable  ten- 
dency to  remember  things  as  coherent  wholes  capable  of  brief 
and  definite  description  and  congruent  with  the  emotion  of 
the  moment. 

As  memory  distorts  the  inner  content  of  an  experience 
itself,  so  it  may  easily  distort  its  relation  to  other  experiences  : 
and  then  \ve  get  the  dates  and  places  wrong.  We  feel  that 
experience  A  must  have  taken  place  in  connection  with  B, 
possibly  because  that  is  the  logical  order,  possibly  because 
we  have  often  thought  of  them  together ;  and  yet  as  a  matter 
of  fact  they  may  have  been  miles  or  months  apart. 

Serious  consequences  often  result  from  this  erroneous 
*  recollection '  of  the  connections  between  experiences  and 
Honest  tne  corresponding  forgetfulness  of  their  real  con- 

lies-  nections.  If  we  remember  a  dream  or  a  fancy 

with  such  vividness  that  it  has  the  feeling  of  reality  and  do 
not  remember  the  outward  relations  that  would  clearly  dis- 
tinguish it  as  a  dream  or  fancy,  it  will  seem  to  us  that  what 
we  are  remembering  is  not  fancy  but  fact,  and  we  easily  fill 
in  the  connections  that  facts  like  those  '  remembered'  ought 
to  have.  Thus  there  are  people  who  lie,  and  lie  habitually, 
with  the  very  best  faith.  The  only  possible  remedy  for 
this  unconscious  lying  is  to  distrust  one's  own  memory  and 
deliberately  test  or  verify  one's  '  recollections  '  in  every  case 
of  importance  ;  and  if  one  does  not  wish  to  be  deceived  by 
others,  he  must  distrust  theirs  too.  Lawyers  are  proverbially 
unsatisfactory  witnesses,  simply  because  they  know  how 
uncertain  memory  is,  and  only  say  'I  think  so',  when  others 
far  less  accurate  and  careful  say  '  I  know  ' ;  and  of  course  the 
confident  assertions  of  the  man  who  '  knows  '  carry  far  more 
weight  with  the  ordinary  juryman  than  the  hesitating  beliefs 
of  the  one  \\ho  only  '  thinks  so  '. 

"  The  medico-legal  aspect  of  this  subject  is  of  the  most 
"practical  importance.  The  more  common  forms  of  param- 
nesia  [or  false  memory]  .  .  .  show  that  it  is  not  impossible 
+.0  manufacture  testimony.  A  member  of  the  bar  tells  me 


HONEST   LIES.  353 

that  this  is  actually  done  in  some  cases,  the  method  employed 
being  somewhat  as  follows  :  The  witness  is  a  person  of 
deficient  memory.  It  is  desirable  that  he  should  testify  to  the 
occurrence  of  a  certain  event.  The  lawyer  asks  the  witness 
if  lie  remembers  this  event.  The  reply  is,  No;  and  nothing 
more  is  said.  But  the  idea  of  the  event  has  been  suggested 
to  the  mind  of  the  witness.  In  a  few  weeks  the  lawyer  re- 
peals the  same  question,  and  again  receives  a  negative  answer. 
But  after  a  few  similar  experiments  the  witness  becomes  un- 
certain whether  he  remembers  the  event  in  question  or 
not.  He  begins  to  think  that  he  does.  The  images  of 
the  imagination  suggested  by  the  lawyer's  questions  loom 
up  vaguely  in  the  mind,  the  memory  is  confused,  and 
in  a  few  months  the  lawyer,  if  skilful,  may  develop  a 
pseudo-reminiscence  so  strong  that  the  witness  will  give 
the  desired  testimony  with  complete  sincerity.  Of  course 
this  cannot  succeed  with  persons  of  strong  memory  and 
critical  judgment,  but  with  children  and  aged  people  it  may 
not  be  difficult.  .  .  . 

"  Nothing,  as  Motet  says,  is  more  effective  than  a  child's 
story  of  the  details  of  a.  crime  of  which  he  pretends  to  have 
been  a  witness  or  a  victim.  The  child's  naivete  adds  to  the 
interest  and  elicits  confidence.  His  hearers  urge  him  on  by 
their  sympathy.  Parents,  friends,  and  neighbors  accept  the 
account,  true  or  false.  They  suggest  new  details  and  fill  up 
the  gaps  in  the  story.  The  child's  uncritical  mind  assimi- 
lates these  details,  repeats  the  story  without  variation,  and 
makes  his  accusation  before  the  magistrate  with  an  apparent 
accuracy  that  is  most  telling.  .  .  . 

"The  uncertainty  of  human  testimony  was  notably  illus- 
trated a  few  years  ago  in  the  case  of  the  Bell  Telephone  Co. 
vs.  the  People's  Telephone  Co.  The  chief  point  at  issue 
was  whether  Daniel  Drawbaugh  had  a  telephone  in  his  shop 
prior  to  1876.  Several  hundred  witnesses  gave  testimony 
bearing  directly  or  indirectly  upon  this  point.  The  honesty 
of  most  of  the  witnesses  seems  to  have  been  admitted,  yet 


354  OBSERVATION   AND   MEMORY. 

evidence  offered  by  one  side  was  generally  refuted  by  testi- 
mony from  the  other.  The  Supreme  Court  divided  upon  the 
case,  and  the  seven  thousand  printed  pages  of  evidence  in  the 
suit  seem  rather  to  prove  the  fallibility  of  human  testimony 
than  anything  else.  See  article  on  Daniel  Drawbaugh,  by 
H.  C.  Menvin,  Atlantic  Monthly,  Sept.,  1888."  * 

Since  memory  is  always  unreliable,  almost  the  first  thing 
for  one  who  is  doing  scientific  work  of  any  sort,  no  matter 
how  humble,  to  learn  is  the  importance  of  keeping 
common-  full  and  clear  records  of  every  detail  of  his  experi- 
ments or  observations  that  may  have  the  slightest 
bearing  on  the  question  at  issue.  If  a  detail  is  to  be  pre- 
served at  all,  it  must  be  taken  down  at  once  ;  it  is  usually 
almost  as  easy  to  take  down  a  point  of  doubtful  value  as  to 
neglect  it,  and  the  best  and  most  accurate  of  experimenters 
are  only  too  liable  to  find  their  work  less  valuable  than  it 
might  otherwise  have  been  because  there  was  some  small 
detail  of  which  they  did  not  make  a  note.  Most  beginners 
need  to  be  warned,  too,  not  to  keep  notes  on  loose  scraps  of 
paper,  not  to  use  unfamiliar  abbreviations  without  writing 
down  their  meaning,  and  to  make  their  writing  very  legible. 
If  they  themselves  are  to  be  sure  of  its  meaning,  the  record 
should  be  so  clear  and  unambiguous  that  it  could  be  easily 
understood  by  any  one.  In  other  words,  it  should  be  a  true 
record,  and  not  a  mere  series  of  suggestions  for  the  memory. 
It  is  important,  too,  to  number  the  pages  (unless  the  record 
is  in  a  book;  and  to  leave  plenty  of  blank  space  on  each  of 
them.  There  is  a  strong  tendency  to  get  things  crowded 
some  time  or  other  before  the  results  are  finally  computed, 
and  a  crowded  record  is  very  confusing.  Finally,  the  notes 
should  be  indexed  and  put  away  in  such  order  that  they  can 
be  found  at  a  moment's  notice  for  years  afterwards.  To 
observe  these  simple  precautions  is  to  save  much  time  and 
annoyance  for  everybody  concerned ;  and  what  is  said  here 

*  W.  II.  Burnham,  loc.  cit. 


RESULTING   COMMONPLACES.  355 

about  scientific  work  is  just  as  true,  mutatis  mutandis,  of  a 
fanner  trying  to  remember  what  his  fields  have  done  each 
year,  or  of  business,  school-teaching,  housekeeping,  or  any- 
thing else  where  it  is  worth  while  to  remember  transactions 
accurately. 


CHAPTER  XXXIV. 

THE    DISCOVERY    OF   PAST    AND   FUTURE  EVENTS    IN 
GENERAL. 

WHEN  we  wish  to  ascertain  some  specific  fact  that  we  have 
not  been  able  to  observe  for  ourselves  there  are  only  two  ways 
of  doing  it.  One  is  to  depend  upon  the  testimony  of  others  ; 
and  the  other  is  to  draw  an  inference  from  what  we  know  of 
the  general  laws  of  nature  ami  the  specific  facts  that  we  or 
others  have  observed.  The  latter  method  can  be  described 
very  briefly,  and  so  \ve  shall  speak  of  it  first.  This  is  the 
method  used  in  tracing  the  history  of  the  solar  system  from, 
or  rather  back  to,  the  vapor  and  the  star-dust  from  which  the 
planets  were  made  and  in  prophesying  the  condition  of  cold 
and  darkness  and  lifelessness  to  which  they  may  be  destined. 
It  is  the  method  pursued  by  geology  in  tracing  the  changes 
which  have  taken  place  on  the  earth's  crust  and  prophesying 
those  which  will  take  place.  And  it  is  the  method  pursued 
by  evolutionary  biology  in  tracing  the  history  of  life  in  the 
world  as  it  has  developed  from  one  form  to  another.  In  all 
these  sciences  the  starting-point  is  the  present,  and  the  ques- 
tion is  always  this:  Granting  the  truth  of  the  general  la\\s 
assumed  or  ascertained  by  various  sciences,  what  is  the  only 
concrete  state  of  affairs  that  could  have  preceded  the  one 
which  we  observe  to  exist  at  the  present,  and  what  is  the 
only  concrete  state  of  affairs  that  can  succeed  it? 

The  first  thing  to  notice  about  this  method  is  that  we 

356 


THE   STARTING-POINT.  357 

always  start  from  the  present.  In  telling  about  history  of 
any  sort  we  may  often  begin  '  at  the  beginning  '.  Tne  start  - 
In  investigating  it  we  never  can.  Moreover,  if  ing-point, 
we  are  mistaken  about  some  of  the  general  laws  or  if  we  are 
not  quite  accurate  about  some  of  the  concrete  facts  with 
which  we  start,  the  consequences  of  our  error  will  affect  all 
our  history  and  all  our  prophecy  ;  and  since  there  is  a 
chance  of  overlooking  some  essential  fact  or  making  some 
miscalculation  at  each  stage  of  our  regress  into  the  past  or 
progress  into  the  future,  the  chances  are  that  the  farther  we 
go  the  less  accurate  our  account  of  things  can  be.  The  pos- 
sibility of  such  accumulation  of  errors  will  always  make  a  defi- 
nite and  detailed  description  of  the  world  more  doubtful  the 
farther  the  described  state  of  affairs  is  removed  from  the 
present  data  with  which  we  have  to  start.  But  indeed  what 
we  know  about  the  laws  of  nature  and  present  concrete  con- 
ditions is  so  slight  in  comparison  with  what  we  do  not  know, 
and  even  those  things  that  we  do  know  are  so  enormously 
complex,  that  no  one  really  attempts  to  work  out  the  prob- 
lem in  all  its  details,  and  the  most  that  any  scientist  attempts 
to  tell  about  either  the  distant  past  or  the  distant  future  is 
the  broad  outlines  of  things,  which  would  remain  substantially 
the  same  no  matter  what  were  true  about  anyone  of  countless 
smaller  details.  A  geologist  can  tell  with  perfect  confidence 
that  where  there  is  now  a  certain  group  of  hills  there  was 
once  a  fairly  level  plateau,  and  he  can  tell  that  the  change 
from  one  to  the  other  was  due  in  the  main  to  the  action  of 
water  running  down  to  the  valley  below,  but  he  would  never 
attempt  to  tell  the  exact  location  of  every  stream  or  the 
amount  of  earth  that  one  of  them  carried  down  on  some  par- 
ticular day  ten  thousand  years  ago. 

Even  what  a  geologist  does  tell  about  the  past  and  the 
future  is  not  based  upon  the  most  ultimate  laws  of  matter 
known.  If  it  were,  he  would  have  deduced  the  history  of 
the  world  from  the  known  laws  of  chemistry  and  molecular 
physics;  and  such  deduction  is  impossible  because  the  situ- 


358   THE   DISCOVERY   OF    PAST   AND   FUTURE   EVENTS. 

ations  that  these  sciences  deal  with  are  exceedingly  simple,  and 
from  the  relations  that  are  found  to  exist  in  these  simple  sit- 
uations no  one  could  possibly  calculate  what  would  happen 
under  the  vastly  more  complex  conditions  that  are  dealt  with 
in  geology.  The  geologist  starts  rather  with  '  empirical 
laws  '  which  are  much  less  precise  (^o  far  as  particular  mole- 
cules are  concerned)  than  the  laws  of  molecular  physics,  but 
which  give  a  much  better  idea  of  what  happens  when  things 
are  arranged  as  he  supposes  them  to  be  in  the  large.  He  sees, 
for  example,  that  streams  actually  do  wear  away  earth  and 
rock  from  their  beds  and  carry  the  debris  away,  and  he  de- 
termines by  actual  measurement  the  amount  of  earth  of  a 
given  kind  that  a  stream  of  a  given  si/.e  and  swiftness  carries 
off  in  a  given  length  of  time  ;  and  then  he  applies  the 
'empirical  law'  which  he  derives  from  such  measurements 
directly  to  the  problem  in  hand.  He  knows,  of  course, 
that  the  facts  in  the  case  are  consistent  with  molecular  physics, 
but  he  knows  also  that  his  data  are  much  too  crude  and 
complex  to  be  dealt  with  by  that  science  ;  and  so  he  works 
away  with  his  '  empirical  laws  '  in  comparative  oblivion  of  it. 
Almost  all  of  our  history  of  the  world  and  our  prophecy  of 
its  future  is  based  upon  such  '  empirical  laws '  as  these, 
derived  from  a  view  of  things  in  the  large;  and  of  course 
any  history  or  prophecy  which  is  based  altogether  upon  such 
broad  rough  laws  cannot  attempt  to  describe  small  details. 

Another  thing  to  notice  about  scientific  history  and  proph- 
ecy is  that  there  is  nothing  in  the   laws  and   concrete  facts 

upon  which   they  are  based   to  tell    the  scientist 
The  limit.  .     .  ., 

when   the  whole  world-process  began  or  when  it 

will  come  to  an  end.  For  all  we  know  or  ever  could  know, 
God  may  annihilate  the  whole  world  to-morrow  ;  but  our 
prophecy  based  on  laws  and  concrete  facts  of  the  present  looks 
forward  without  limit  towards  a  whole  eternity.  In  the  same 
way  we  trace  what  we  suppose  to  be  the  broad  outlines  of  his- 
tory further  and  further  into  the  past,  and  we  never  reach  and 
never  can  reach  a  point  at  which  we  can  say  :  Here  everything 


'MONUMENTS.'  359 

must  have  begun.  If  the  world  ever  was  made  and  wound  up 
like  a  watch,  whether  five  thousand  years  ago,  as  theologians 
used  to  suppose,  or  twenty-four  hours  ago,  \ve  can  never  see 
anything  on  the  face  of  it  to  indicate  when  that  took  place. 
All  we  can  say  is  that  if  this  world-watch  really  was  going  six 
thousand  years  ago  as  it  is  going  now,  then  at  precisely  that 
time  the  hands  were  in  such  and  such  a  position. 

It  seems  much  easier  to  believe  that  the  world  started  five 
thousand  or  five  billion  years  ago  than  twenty-four  hours  ago, 
merely  because  our  whole  conception  of  so  distant  a  past  is 
vaguer.  But  if  it  started  five  thousand  years  ago,  it  started 
with  fossils  in  the  rocks  and  all  the  other  absolutely  definite 
conditions  that  must  have  preceded  the  present  and  that  lead 
scientists  to  trace  its  history  beyond  the  five  thousand  years 
of  its  actual  existence.  And  if  it  started  five  billion  years  ago, 
every  detail  must  have  been  just  as  definite  ;  however  hazy 
our  idea  of  it  may  be.  It  might  just  as  well  have  been  cre- 
ated twenty-four  hours  ago  with  mines  half  empty  and  cities 
all  built  and  ships  in  the  harbors,  and  adult  human  beings 
busy  at  their  work,  with  brains  so  fashioned  that  they  look 
back  towards  an  imaginary  past  and  believe  they  remember 
it.  Thus,  starting  from  the  present  as  science  does  and  must, 
and  assuming  as  it  does  that  things  acted  in  the  past  and  will 
act  in  the  future  according  to  the  same  laws  that  we  find  now, 
it  is  quite  impossible  for  us  to  find  any  point  at  which  the 
world-process  must  have  begun  or  must  come  to  an  end,  even 
if  there  really  was  such  a  beginning  and  really  will  be  such  an 
end. 

One  might  think    that  the  uncertainty   due    to  the   frag- 
mentary nature  of  our  knowledge  and  this  possible  accumula- 
tion of  errors  should  affect  our  knowledge  of  the    ,  Monu_ 
past  quite  as  much  as  our  knowledge  of  the  future  ;    ments.' 
but  as  a  matter  of  fact  it  does  not.      We  know  a  great  deal 
more  about  the  past ;   and  the  reason  is  that  many  conditions, 
when  they  are  once  produced,  remain  practically  unaltered 
for  a  great  many  years.     No  geologist  can  tell  whether  the 


360   THE   DISCOVERY   OF   PAST   AND    FUTURE   EVENTS. 

place  where  I  am  now  writing  will  ever  be  covered  with 
water  or  not  ;  but  from  the  layer  of  gravel  beneath  the  sur- 
face of  the  ground  I  can  infer  with  reasonable  certainty  that 
once  it  was.  No  one  can  tell  whether  Vesuvius  will  ever  de- 
stroy a  city  again,  but  from  the  buried  remains  of  Pompeii 
and  from  written  records  \ve  can  infer  that  once  it  did.  This 
is  merely  because  we  have  reason  to  believe  that  such  things 
as  beds  of  gravel,  the  stones  of  buried  cities  and  forgotten 
documents  remain  comparatively  unchanged  for  years  or  cen- 
turies. Thus  when  we  find  such  things  they  take  us  at  one 
leap  beyond  all  the  intervening  years,  and  each  of  them 
shows  us  one  fragment  of  the  past  as  it  existed  at  the  time. 

Accordingly,  if  we  are  right  in  assuming  that  such  relics  of 
the  past  have  remained  unaltered  in  any  given  respect,  and 
if  we  have  any  means  of  finding  out  their  age,  we  can  use 
each  one  of  them  as  a  starting-point  in  the  construction  of 
the  past,  or  at  least  as  something  fixed  by  which  to  test  our 
inferences  about  it.  In  such  cases  we  might  almost  say  that 
we  really  do  start  with  the  past.  This  is  why  we  can  tell 
more  about  some  things  in  the  past  than  in  the  future  ;  why 
there  is  such  a  thing  as  serious  history  where  there  is  no 
corresponding  prophecy. 

It  is  because  there  are  such  absolutely  or  relatively  perma- 
nent '  monuments  '  of  the  past  as  these  that  it  is  possible  for 
us  to  distinguish  between  relatively  direct  evidence  concern- 
ing past  events  and  indirect.  The  most  direct  evidence  con- 
cerning any  event  is,  of  course,  the  present  and  personal 
perception  of  the  event  itself.  This  is  something  independ- 
ent of  'monuments  '  of  any  sort,  but  if  the  event  is  past,  this 
evidence  is  unattainable.  The  most  direct  evidence  then 
possible  is  the  perception  of  something  which  we  can  assume 
to  be  a  direct  effect  of  the  event,  and  after  jthat  the  supposed 
effects  of  effects  of  the  event  or  the  supposed  effects  of  some- 
thing that  would  have  caused  the  event ;  until  the  chain  is  as 
long  or  crooked  as  you  please.  The  most  direct  evidence  of 
the  destruction  of  Pompeii  by  a  volcanic  eruption  would  be 


CIRCUMSTANTIAL   EVIDENCE.  361 

the  perception  of  the  event  itself.  The  most  direct  evidence 
possible  for  us  is  the  personal  perception  first  of  the  unbroken 
lava  and  then  of  the  houses  being  dug  out  from  beneath  it. 
Photographs  of  such  lava-beds  and  houses  give  less  direct 
evidence,  and  the  tales  of  persons  who  claim  to  have  seen 
such  photographs  less  direct  still. 

It  is  hardly  necessary  to  add  that  the  most  reliable  evi- 
dence about  past  events  is  afforded  by  monuments  which  we 
know  to  have  undergone  the  least  possible  change,  and  which 
are  connected  with  the  events  under  investigation  by  the 
shortest  and  surest  series  of  causal  relations.  The  value  of 
written  records  as  monuments  of  the  past  will  be  spoken  of 
in  the  next  chapter. 

One  hears  a  great  deal  in  discussions  of  criminal  trials 
about  circumstantial  evidence.  Evidence  is  called  xcircum- 
stantial  when  the  witnesses  have  not  observed,  Circum- 
and  therefore  cannot  tell  about,  the  very  fact  at  evidence. 
issue  {e.g.,  A  murdering  B),  but  can  and  do  tell  about 
various  other  facts  so  connected  with  the  fact  at  issue  by  the 
law  of  causation  that  from  them  the  jury  can  infer  what  that 
fact  really  was.  Thus  '  circumstantial  evidence  '  is  only  the 
common  name  for  indirect  evidence  of  the  sort  that  may  be 
given  in  a  court  of  law.  If  A  and  B  were  heard  talking 
loudly  as  though  they  were  in  a  violent  dispute  and  if  A  was 
afterwards  seen  leaving  the  house  covered  with  blood,  while 
B  was  found  stabbed  to  the  heart  with  A's  knife,  there  would 
be  good  circumstantial  evidence  that  A  had  killed  him,  and 
he  might  very  well  be  convicted  and  hanged  for  a  crime  that 
no  one  had  seen  him  commit. 

Circumstantial  evidence  is  conclusive  only  if  a  supposed  state 
of  affairs  is  the  only  one  that  will  fit  in  with  the  ascertained 
facts  according  to  the  general  laws  of  nature.  In  a  simple 
case  of  astronomy  or  chemistry  a  conclusion  of  this  sort  can 
be  drawn  with  practical  certainty  ;  but  with  human  affairs 
the  case  is  somewhat  different ;  for  human  life  and  the  con- 
ditions that  determine  it  are  so  exceedingly  complex  that  it 


362    THE   DISCOVERY   OF   PAST   AND    FUTURE   EVENTS. 

is  very  rarely  possible  to  say  with  anything  like  certainty  : 
This  supposed  state  of  affairs  and  this  alone  is  consistent 
with  all  the  established  facts.  In  the  case  given,  for  example, 
it  is  quite  possible  that  B  was  seized  with  a  sudden  mania 
during  which  he  first  picked  a  quarrel  with  A  and  then  seized 
A's  knife  and  stabbed  himself,  while  the  blood  on  A  was  due 
to  his  efforts  to  prevent  B  from  doing  the  mad  deed.  Or  it 
might  be  that  A  and  B  were  not  quarrelling  with  each  other 
but  with  some  third  person,  who  had  afterwards  picked  up 
the  knife,  committed  the  murder  and  then  made  his  escape. 
Or  the  real  truth  of  the  matter  might  be  something  entirely 
different  that  nobody  happens  to  think  of  at  all.  A  person 
convicted  of  some  crime  on  circumstantial  evidence  is  thus 
often  convicted  on  a  degree  of  probability  which  falls  con- 
considerably  short  of  practical  certainty  ;  which  means,  of 
course,*  that  amongst  a  large  number  of  such  cases  there  are 
a  few  in  which  the  person  convicted  and  punished  is  really 
innocent.  This  accounts  for  the  general  feeling  of  uneasiness 
or  dissatisfaction  when  a  trial  of  vital  importance  is  decided 
altogether  upon  circumstantal  evidence.  But  we  must  re- 
member that  the  uncertainty  of  a  conclusion  based  upon  such 
evidence  is  due  to  the  complexity  of  the  situation  dealt  with 
and  our  ignorance  of  many  of  its  details,  not  to  a  defect  in 
the  general  principle  ;  for  the  principle  is  that  involved  in  all 
indirect  evidence,  and  it  is  the  only  one  in  virtue  of  which 
we  can  gain  any  knowledge  whatever  of  either  the  past  or 
the  future. 

*  See  p.  334. 


CHAPTER  XXXV. 

TESTIMONY. 

AMONGST  the  most  important  monuments  of  past  events  are 
the  impressions  made  by  them  on  the  minds  of  persons  who 
were  present  at  the  time.  From  these  impres-  its  impor- 
sions,  if  we  can  find  out  what  they  are,  we  can  often  tance- 
judge  the  nature  of  the  events  that  made  them.  Yet  the  im- 
pressions in  the  minds  of  others  can  never  be  observed  directly, 
but  only  inferred  from  what  they  say  and  do.  Hence  there  is 
always  a  double  inference:  from  what  a  witness  says  to  his 
thoughts,  and  from  his  thoughts  to  the  events  that  caused  them. 
The  necessity  for  this  double  inference  often  makes  the  correct 
estimation  of  testimony  very  difficult ;  and  yet  in  all  matters 
of  history — whether  they  be  the  events  of  last  week  told  in  a 
police  court  or  the  events  of  two  hundred  years  ago  set  forth 
in  a  formal  treatise — its  proper  estimation  is  most  important. 
If  we  estimate  it  wrongly  we  are  bound  to  reach  false  conclu- 
sions; and  if  we  ignore  it  altogether  we  can  hardly  reach  any 
conclusions  at  all,  for  apart  from  the  memories  of  men  and 
what  they  have  written  we  have  very  few  unaltered  monu- 
ments of  the  past  life  of  individuals,  and  our  human  environ- 
ment is  so  complex  and  our  knowledge  of  human  nature  so 
slight  that  an  investigator  who  tried  to  find  out  about  the  past 
deeds  of  anybody  else  merely  by  going  back  step  by  step  from 
his  own  personal  experiences  would  hardly  get  started  before 
he  had  to  stop. 

Even  if  there  were  plenty  of  other  evidence,  reliable  testi- 

363 


364  TESTIMONY. 

mony  would  still  have  a  great  and  very  unique  value.  It  sets 
the  whole  scene  before  us,  presumably  as  \ve  our- 
vaiueand  selves  would  have  seen  it  if  we  had  been  there, 
with  the  important  details  accented  and  the  mean- 
ingless trivialities  omitted  or  properly  subordinated;  and  thus 
without  much  trouble  on  our  part  it  gives  us  a  warm,  human, 
unified  account  of  the  whole  matter  at  a  single  sitting,  in- 
stead of  leaving  us  coldly  and  laboriously  to  construct  it  all 
bit  by  bit  from  various  remnants  of  impersonal  evidence  that 
give  the  trivial  and  the  important  all  together  and  leave  us  to 
find  out  what  are  the  points  of  essential  human  interest  for 
ourselves.  In  this  way  testimony  enables  us  to  reap  the  fruits 
of  some  one  else's  perceptions  and  inferences.  But  this  has 
its  dangers,  for  it  tends  to  put  us  at  his  mercy  if  he  chooses 
(as  mere  inanimate  relics  of  the  past  cannot)  to  deceive  us, 
and  to  make  us  share  his  errors  if  his  perceptions,  inferences, 
or  memories  were  wrong.  How  then  can  we  be  sure  in  any 
particular  case  that  there  is  no  mistake  and  no  falsehood,  and 
that  the  words  of  the  witness  have  therefore  given  us  anything 
like  the  idea  of  the  matter  in  question  that  we  should  have 
had  if  we  had  observed  it  for  ourselves;  and  if  we  cannot 
be  sure  of  this,  how  can  we  make  use  of  testimony  at  all? 

It  is  easier  to  answer  this  question  now  than  it  would  have 
been  while  we  were  discussing  the  inductive  methods  by 
which  we  learn  the  laws  of  nature  ;  for  throughout  the  whole 
discussion  we  simply  took  for  granted  that  when  people  are 
working  together  for  a  common  end  they  trust  each  other,  and 
have  a  logical  right  to  do  so.  Xow  that  the  question  is  raised 
we  shall  find  that  in  cverv  specific  case  the  answer  depends 
upon  our  knowledge  of  these  very  laws  that  we  learned 
largely  through  the  aid  of  our  spontaneous  faith  in  one  another. 
The  weighing  of  testimony  involves  some  departure  from 
Ac  ti  the  attitude  that  we  take  most  naturally  and  spoil- 

rejecting,^     taneously  towards  the  stories   that  are  told   to   us. 
in£-  Our  first   natural  attitude  towards   testimony  is 

one  of  trust ;   not  because   we  have  reasoned  that  it  is  trust- 


ACCEPTING,  REJECTING,   AND    WEIGHING.  365 

worthy,  but  merely  because  we  cannot  help  it.  If  it  had  not 
always  been  natural  to  accept  the  statements  of  those  about  us 
as  substantially  true,  we  should  probably  not  be  alive  now  to 
discuss  the  matter;  for  the  telling  of  the  truth  on  the  one  hand 
and  confidence  in  the  story  told  on  the  other  are  very  impor- 
tant means  for  the  preservation  of  the  race.  Each  of  us  is  born 
into  a  larger  or  smaller  community  with  common  interests  : 
a  common  living  to  gain,  common  diseases  to  avoid,  and 
common  enemies  to  overcome.  We  can  attain  these  common 
aims  only  by  co-operation,  and  we  cannot  co-operate  intel- 
ligently unless  we  all  have  approximately  the  same  ideas.  In 
warfare  the  chief  must  rely  upon  the  scouts  for  knowledge  of 
the  position  and  numbers  of  the  enemy,  and,  on  peril  of  its 
existence,  the  whole  tribe  must  act  upon  that  knowledge  as 
the  chief  commands.  A  sceptic  who  refused  to  believe  and 
obey  would  be  likely  to  sacrifice  his  o\vn  life  and  perhaps 
that  of  the  tribe  as  well  to  his  rebellious  incredulity;  and  so 
likewise  with  the  chase,  sanitation,  and  other  relations  of  life. 
Since  we  are  all  fitted  for  this  life  in  common  it  is  almost 
as  natural  for  us  to  share  the  ideas  of  our  friends  as  to  share 
their  interests,  and  to  accept  the  beliefs  of  those  in  authority 
as  to  obey  their  commands.  Indeed  it  is  no  accident  that 
the  words  Yes  and  No,  which  are  used  to  express  obedience 
or  consent  and  their  reverse,  are  also  used  to  express  intel- 
lectual assent  and  dissent,  and  that  such  words  as  Ally,  Op- 
ponent, Our  Side,  Their  Side,  Attack,  Rescue,  Beaten,  Vic- 
tor, are  used  as  much  with  reference  to  a  '  conflict '  about 
some  matter  of  opinion  as  to  any  other,  however  deadly.* 

*  This  need  for  a  community  of  thought  within  the  tribe  as  well  as  of 
action  is  expressed  in  many  ways.  In  the  heat  of  a  military  or  political 
campaign  a  man  who  says  that  his  country  or  his  party  is  in  the  wrong 
is  branded  as  a  traitor.  In  religion  the  demand  for  uniformity  of  belief 
has  shown  itself  in  state  churches  with  their  old-time  persecution  of 
heretics  and  the  modern  prosecutions  for  heresy,  in  the  maintenance  of 
our  various  Protestant  sects  on  a  community  of  creeds  rather  than  of 
aspirations,  and  in  the  feeling  we  often  find  that  even  though  a  belief  be 
true  it  is  wrong  to  accept  it  if  the  Church  says  otherwise.  Even  social 


366  TESTIMONY. 

Along  with  this  tendency  to  accept  without  question  the 
statements  of  those  whom  we  love  and  honor  there  soon  grows 
up  the  tendency  to  reject  the  statements  (whether  we  believe 
them  to  be  sincere  or  not)  of  those  whom  we  hate  or  despise. 
*  The  truth  for  friends  and  lies  for  enemies.'  This  is  a  good 
rule  of  tribal  policy  and  one  so  often  followed  that  even  in 
modern  warfare,  and  often,  too,  in  modern  diplomacy,  we  ex- 
pect the  enemy  to  deceive  us  if  he  can.  Even  when  we  are 
sure  that  we  know  the  real  beliefs  and  institutions  of  another 
tribe,  we  feel  that  they  cannot  be  accepted  without  disloyalty 
to  our  own.  If  any  one  is  a  foreigner  or  an  '  Outlander',  that 
is  enough  to  make  his  language,  his  clothing,  his  customs,  and 
his  religion  all  'outlandish  '.  We  do  not  weigh  his  opinions 
any  more  than  we  consider  his  interests ;  we  simply  reject 
them  with  contempt.  In  the  same  way  with  private  individuals 
within  the  family,  the  tribe,  the  nation,  or  the  church,  if  they 
antagonize  us  it  is  almost  a  point  of  honor  with  us  to  dis- 
prove, or  at  least  to  disbelieve,  everything  they  say.  Thus 
we  tend  to  accept  the  statements  and  the  real  beliefs  of  our 
friends  and  to  reject  those  of  our  enemies;  but  not  to  weigh 
either  the  one  or  the  other. 

This  rough  instinctive  way  of  accepting  and  rejecting 
testimony  is  good  enough  in  the  main  for  children  and  for 
the  plain  men  and  women  who  are  content  or  compelled  all 
their  life  to  follow  the  lead  of  others,  if  the  leaders  are  already 
given.  But  it  is  not  sufficient  when  there  is  a  conflict  of 
authorities  and  one  has  to  choose  his  leader.  It  is  not  suf- 
ficient either  when  a  person  wishes  to  go  without  a  leader 
and  perhaps  to  become  a  leader  himself;  that  is  to  say,  \\hen 
he  differentiates  himself  from  the  rest  of  the  set,  whether  it 

classes  tend  to  have  their  own  characteristic  beliefs,  and  one  rejects 
those  of  another  without  argument  as  visionary,  aristocratic,  or  vulgar. 
Science  it?e!f  is  not  free  from  the  same  influence,  for  there  are  different 
'schools'  of  philosophy  and  medicine  as  well  as  of  theology,  and  an 
odiiiin  inedicum  as  well  as  an  odium  theologicitm.  The  whole  tendency 
can  be  summed  up  in  the  common  use  of  the  phrase  I'ox populi  vox  Dei. 


EXPERT   EVIDENCE.     CAUTION.  367 

be  family,  tribe,  nation,  church,  or  social  clique,  and  feels 
that  he  has  interests  which  the  others  do  not  share,  or  feels 
that  he  knows  more  than  the  rest  or  observes  more  carefully 
or  has  better  natural  judgment  or  a  better  standpoint  from 
which  to  judge.  A  person  in  either  of  these  situations  who 
has  testimony  to  deal  with  and  who  wishes  to  act  rationally 
must  try  to  settle  his  problem  for  himself  in  the  light  of 
what  he  already  knows  about  the  world  and  its  laws. 

In  the  first  situation  he  must  weigh  as  best  he  can  the 
merits  of  the  rival  authorities.  That  is  to  say,  he  must  try  to 
find  out  what  causes  would  naturally  make  a  person  an  author- 
ity on  such  matters  and  then  inquire  how  many  of  these  were 
present  in  the  case  of  each  of  the  claimants.  In  the  second 
situation,  where  he  is  trying  to  find  the  truth  through  testi- 
mony about  some  matter  without  the  appeal  to  any  authority, 
he  must  '  weigh  '  the  testimony  itself.  This  simply  means 
that  he  must  treat  all  the  testimony  on  the  matter  as  an  effect 
and  inquire  what  causes  could  have  produced  it.  In  either 
case  he  must  settle  his  question  by  an  appeal  to  the  known 
uniformities  of  Nature  ;  and  if  he  does  not  assume  that  Nature 
is  uniform,  he  cannot  settle  it  rationally  at  all.5'5 

When  the  question  at  issue  is  one  about  which  we  cannot 
hope  to  judge  altogether  for  ourselves  because  a  wholly  inde- 
pendent judgment  requires  technical  knowledge 

0  ,    Expert 
of  a  sort  that  we  do  not  possess,  we  must  appeal    evidence. 

for  aid  to  those  who  do  possess  such  knowledge  ; 
but   we   must   take  care   to  avoid  the    fallacy  known  as  the 
'Argument  from   Authority'  (Argumenium  ad  Vcrccundiani). 
This  expression  does  not  mean  that  every  appeal  to  authority 
is   fallacious.     The    fallacy  arises  only  when,  awed  perhaps 

*  By  finding  the  truth  in  a  case  of  this  sort  we  mean  finding  what  we 
ourselves  should  have  perceived  if  we  had  been  present,  or  what  would 
have  been  perceived  by  some  one  else  who  shares  our  interests  and  has  at 
least  as  good  natural  ability  and  training.  We  do  not  mean  finding  the 
absolute  truth,  as  God  might  perceive  it  ;  for  very  likely  that  would  not 
fit  into  our  general  conception  of  the  world  at  all. 


368  TESTIMONY. 

by  the  greatness  of  a  name,*  we  accept  as  expert  opinion  the 
dictum  of  some  one,  however  great  in  some  other  direction, 
who  is  not  an  expert  on  the  matter  in  question.  A  minister's 
training  may  fit  him  to  speak  with  authority  about  the  world 
to  come,  but  not  about  the  value  of  a  patent  medicine.  A 
barber  knows  how  to  cut  hair,  but  that  gives  him  no  special 
skill  in  preparing  a  hair-tonic.  A  great  scientist  is  not  nec- 
essarily an  authority  on  metaphysics ;  a  great  philosopher 
(such  as  Kant  or  Hegel),  on  the  history  of  philosophy  ;  a 
great  soldier,  on  politics;  or  a  successful  evangelist  on 
Church  history  or  Biblical  criticism.  '  Practical  business 
men '  often  speak  with  scorn  of  the  '  theorists '  who  differ 
from  them  on  economic  questions,  though  the  very  necessity 
for  knowing  the  details  of  their  own  business  may  keep  such 
men  from  seeing  the  general  relations  of  all  a  country's  in- 
dustries. A  telescopic  survey  of  the  world  is  called  for,  and 
they  claim  to  speak  with  authority  because  they  have  a 
microscopic  knowledge  of  a  corner  in  a  city  lot  ! 

Similarly  a  scientist  who  is  great  because  of  his  power  to 
collect  facts  may  be  a  poor  interpreter  of  them  ;  just  as  a 
skilful  census-enumerator  might  be  utterly  unable  to  explain 
a  single  figure  in  the  returns. 

This  is  a  fallacy  which  one  can  never  be  sure  of  avoiding, 
unless  he  sets  out  to  believe  nothing  at  all.  The  great  thing 
is  to  select  one's  experts  with  proper  care  and  then  trust  them 

*  "  Even  proper  names  themselves  do  not  seem  always  spoken  with  a 
design  to  bring  into  our  view  the  ideas  of  those  individuals  that  are  sup- 
posed to  he  marked  by  them.  For  example,  when  a  schoolman  tells  me 
'  Aristotle  hath  said  it ',  all  I  conceive  he  means  by  it  is  to  dispose  me 
to  embrace  his  opinion  with  the  deference  and  submission  which  crstom 
has  annexed  to  that  name.  And  this  effect  is  often  so  instantly  pro- 
duced in  the  minds  of  those  that  are  accustomed  to  resign  their  judg- 
ment to  authority  of  that  philosopher,  as  it  is  impossible  any  idea  either 
of  his  person,  writings,  or  reputation  should  go  be  tore.  So  close  and 
immediate  a  connection  may  custom  estaLli.-h  between  the  verv  word 
Aristotle  and  the  motions  of  assent  and  reverence  in  the  minds  of  some 
men.'"  (Berkeley,  "Principles",  Introduction.) 


EXPERT    EVIDENCE.     CAUTION.  369 

only  where  they  are  strong.  When  selected  the  best  of  them 
will  often  be  found  to  have  marked  tendencies  in  one  direc- 
tion or  another — "personal  equations" — for  which  due 
allowance  must  be  made.  We  see  best  the  side  of  things, 
with  which  we  are  most  familiar  and  in  which  we  are  most 
interested.  It  is  thus  natural  enough  that  a  physician,  for 
example,  should  find  nothing  but  physical  disease  behind 
some  act  that  a  clergyman  might  attribute  altogether  to  sin. 
Indeed  physicists  and  biologists  often  tend  to  ignore  such  a 
thing  as  conscious  thought  altogether  or  to  treat  it  as  a  mere 
by-product  of  bodily  life,  while  idealistic  philosophers  return 
the  compliment  by  ignoring  or  denying  the  existence  or  the 
influence  of  the  body.  So,  turning  from  training  to  tem- 
perament, a  cruel  man  skilled  in  statecraft  might  advocate 
a  measure  of  which  a  humane  man  equally  skilled  might 
wholly  disapprove.  Then,  too,  personal  interest  often  affects, 
our  judgment,  not  because  we  wish  it  to,  but  because  it  keeps 
us  constantly  thinking  of  our  own  side  of  the  case,  which 
consequently  gets  well  thought  out,  while  the  other  sides  does 
not.  In  the  Southern  States,  where  economic  conditions, 
made  slavery  profitable,  it  was  regarded  as  a  divine  institu- 
tion ;  in  the  North,  where  economic  conditions  had  crowded 
it  out,  it  was  regarded  as  diabolical.  Such  interests  are  likely 
to  affect  experts  as  well  as  others. 

Three  specially  flagrant  kinds  of  fallacious  arguments  from 
authority  are  what  Whately  calls  the  Fallacy  of  References, 
the  appeal  to  what  Minto  calls  the  Abstractly  Denominated 
Principle,  and  what  we  may  call  the  Appeal  to  an  Imaginary 
Expert. 

The  first  of  these,  which,  according  to  Whately,  is  "  par- 
ticularly common  in  popular  theological  works",  consists 
in  making  a  great  show  of  scriptural  or  other  authority  for 
some  particular  doctrine  by,  not  quoting,  but  merely  giving 
references  to  a  large  number  of  passages  that  have  some 
bearing  or  other  upon  the  subject,  though  few  or  none 
of  them  "distinctly  and  decidedly"  favor  the  opinion  in 


370  TESTIMONY. 

question;  "  trusting  that  nineteen  out  of  twenty  readers  will 
never  take  the  trouble  of  turning  to  the  passages,  but,  taking 
for  granted  that  they  afford,  each,  some  degree  of  confirma- 
tion to  what  is  maintained,  will  be  overawed  by  seeing  every 
assertion  supported,  as  they  suppose,  by  five  or  six  Scripture- 
texts  ". 

In  the  appeal  to  the  Abstractly  Denominated  Principle, 
*'  A  conclusion  is  declared  to  be  at  variance  with  the  princi- 
ples of  Political  Economy,  or  contrary  to  the  Doctrine  of 
Evolution,  or  inconsistent  with  Heredity,  or  a  violation  of 
the  sacred  principle  of  Ereedom  of  Contract"  (Minto) ;  or 
appeal  is  made  to  the  Monroe  Doctrine  or  the  Rights  of 
Man  or  the  Law  of  Nature  or  the  Nature  of  God,  or  anything 
else  that  is  vague,  but  high-sounding  and  terrifying.  "  It  is 
assumed  that  the  hearer  is  familiar  with  the  principle  referred 
to",  though  it  may  well  be  that  neither  hearer  nor  speaker 
really,  knows  anything  about  it.  The  only  thing  for  the 
hearer  to  do  in  such  a  case  is  to  stand  his  ground  and 
frankly  confess  his  ignorance,  if  he  is  ignorant,  and  demand 
an  explanation  of  the  principle  and  of  its  precise  bearing  on 
the  question  at  issue.  But  this  often  requires  great  courage. 

As  an  example  of  an  appeal  to  an  abstractly  denominated 
principle  we  may  perhaps  take  the  argument  of  Cardinal 
Manning  against  vivisection.  It  runs  somewhat  as  follows: 

o          o 

'  Truth  of  Nature  must  be  sought  only  by  methods  in 
harmony  with  the  perfection  of  Nature's  God.  Mercy  is 
one  of  the  perfections  of  God.  Vivisection  is  not  in  harmony 
with  perfect  mercy.  Therefore  truth  must  not  be  sought  by 
vivisection.'  To  all  of  which  Professor  Hodge  replies: 
"  How  the  worthy  cardinal  knows  that  vivisection  is  not  in 
harmony  with  God's  perfect  mercy  he  nowhere  explains." 
(PopuLir  Science  Monthly >  Sept.  1896.) 

By  the  appeal  to  an  Imaginary  Expert  I  mean  the  stating 
of  one's  own  opinions  in  such  a  way  that  they  seem  to  carry 
with  them  the  weight  of  expert  testimony,  though  really  no 
expert  is  quoted  at  all.  Benjamin  Kidd's  "Social  Evolu- 


INFERRING   WITHOUT   TRUSTING.  3?l 

tion  ",  for  example,  is  full  of  passages  in  which  the  author's 
opinion  is  backed  up  by  that  of  an  imaginary  future  expert, 
thus:  "  Yet  nothing  can  be  clearer  to  the  evolutionist  when 
he  comes  to  understand  the  nature  of  the  process  in  progress 
throughout  our  history,  than  that  those  ideals  have  been 
and  are  quite  foreign  to  our  civilization"  (p.  142).  "It 
has  been  the  custom  to  attribute  the  success  of  the  Revolu- 
tion to  the  decay,  misrule,  and  corruption  of  these  classes; 
but  history,  while  recognizing  these  causes,  will  probably 
regard  them  as  but  incidental.  Its  calmer  verdict  must  be  ", 
etc.  "  A  fuller  and  franker  recognition  of  the  true  position 
.  .  .  must  apparently  be  one  of  the  features  of  the  work  of 
the  future  historian  who  would  do  justice  to  the  Revolu- 
tion "  (pp.  185-6).  "  At  a  future  time,  when  the  history 
of  the  nineteenth  century  comes  to  be  written  with  that 
sense  of  proportion  which  distance  alone  can  give,  it  will 
be  perceived  that",  etc.  (p.  299;  see  also  pp.  301,  310, 
edition  of  1895). 

Kidd  is  not  the  only  sinner  in  this  respect.  I  have  just 
run  across  the  following  sentences  in  Harper's  Magazine  : 
"  There  were  to  follow  many  more  desperate  encounters.  .  .  . 
But  in  all  probability  the  careful  historian  will  yet  decide  that 
in  shaping  events  which,  step  by  step,  wrought  the  downfall 
of  the  Southern  coalition,  Fort  Done! son  stands  pre-eminent. 

Leaving  this  question  of  how  a  layman  should  deal  with 
the  testimony  of  real  or  alleged  experts  on  matters  about 
which  he  cannot  pass  an  independent  judgment,  let  us  turn 
again  to  the  principles  according  to  which  we  should  deal 
with  testimony  as  to  matters  of  fact  concerning  which  we  are 
not  wholly  incompetent  to  judge  for  ourselves. 

To  find  the  whole  truth  which  lies  behind  a  statement  will 
always  be  impossible  for  a  human  being;  for  that  means  dis- 
covering and  distinguishing  between  all  the 

Inferring: 
innumerable  causes  that  may  have  contributed   without 

.     .         .       trusting. 

more  or  less  to  produce  it.      Our  knowledge  is 

far  too  slight,  our  perceptions  are  far  too,  inaccurate,  and 


37  2  TESTIMONY. 

our  powers  of  calculation  are  far  too  limited  for  this.  To 
find  a  part  of  the  truth  is  a  very  different  matter.  We  can 
often  do  this  by  causal  inquiries  without  raising  the  question 
of  truthfulness — which  seems  so  important  when  we  are 
merely  accepting  or  rejecting  statements — at  all. 

If  a  seedy-looking  stranger  rings  your  door-bell  and  says 
that  he  has  not  had  anything  to  eat  for  three  days,  you  need 
not  inquire  into  his  truthfulness  in  order  to  infer  that  he 
wants  you  to  give  him  something  and  does  not  expect  you 
to  hand  him  over  to  the  police.  In  the  same  way,  if  some 
one  wrote  a  book  that  is  obviously  intended  to  help  a  certain 
cause,  it  is  evidence — whether  he  believed  what  he  said  or 
not — -that  at  the  time  he  wrote,  such  a  cause  existed  and  at 
least  one  person  thought  it  important  enough  to  write  about. 
If  he  told  a  marvellous  tale  to  amuse  his  readers,  we  can  tell 
that  he  expected  readers  and  expected  them  to  be  amused  by 
a  tale  of  that  kind.  If  he  is  hopelessly  prejudiced,  we  can 
conclude  that  in  his  time  it  was  possible  for  that  particular 
kind  of  prejudice  to  exist.  When  he  tells  about  some  event 
of  which  he  was  a  witness  he  may  be  both  careless  and 
untruthful,  and  yet  there  is  always  something  that  he  reveals 
incidentally.  An  eye-witness  may  get  many  of  the  details 
of  a  great  battle  wrong,  but  he  is  not  likely  to  discuss  the 
way  in  which  the  combatants  managed  their  bows  and  arrows 
and  the  manoeuvres  of  the  triremes  if  the  battle  was  really 
fought  with  Maxim  guns  and  .Mauser  rifles  a  hundred  miles 
from  anv  navigable  water;  and  it  is  certain  that  he  will  not 
talk  of  Maxims  and  Mausers  and  ironclads  if  he  lived  in  an 
age  of  bows  and  arrows,  slings,  and  triremes.  IIo\vever 
dishonest  or  prejudiced  or  stupid  a  writer  may  be,  he  cannot 
make  any  statement  whatever  about  things  that  no  one 
thought  of  in  his  time  and  country,  he  cannot  give  his  story 
a  general  background  absolutely  different  from  that  of  lib 
own  direct  or  indirect  experience,  and  he  cannot  write  in  a 
language  that  he  never  heard  or  read. 

To   take  a   more   concrete   illustration  of  the  same  point. 


MORE   REFINED   METHODS.  373 

Suppose  we  have  reason  to  believe  that  Paul  really  made  the 
speech  before  Agrippa  recorded  in  Acts  xxvi.,  but  have  no 
reason  to  believe  that  he  told  the  truth,  we  can  still  infer 
that  Paul  and  Agrippa  were  contemporaries;  that  Paul  was 
a  prisoner  wearing  some  kind  of  'bonds'  (v.  29);  that  he 
had  been  accused  by  certain  Jews  (v.  2)  of  some  offence 
connected,  or  capable  of  being  plausibly  explained  as  con- 
nected, with  their  peculiar  customs  (v.  3)  and  religious  beliefs 
(v.  7),  and  more  particularly  with  his  own  real  or  assumed 
belief  in  the  resurrection  of  the  dead  (v.  8)  and  with  what 
he  represented  as  the  divine  mission  (vv.  15-22)  of  one  Jesus 
of  Nazareth  (v.  9).  If  we  have  no  reason  to  believe  that 
this  speech  was  ever  made,  but  do  know  the  time  and  place 
at  which  the  story  of  the  speech  was  written,  then  we  can 
still  infer  that  at  that  time  and  place  people  knew  the 
names  Paul,  Agrippa,  Festus,  Jesus, Christ,  Satan,  Jerusalem, 
Damascus,  etc. ;  that  they  had  either  heard  of  the  Jews  and 
their  religious  sects  (v.  5)  or  had  invented  the  idea;  that  it 
seemed  to  them  credible  that  a  Jew  might  be  prosecuted  and 
even  put  to  death  (vv.  10,  31)  for  a  religious  belief,  and 
that  a  king  would  listen  to  a  prisoner  in  bonds  who  talked 
of  prophets,  visions,  repentance,  forgiveness  of  sins,  and  the 
resurrection  of  the  dead;  that  at  least  some  of  the  people 
of  the  time  and  place  where  the  story  was  written  knew  the 
meaning  of  the  common  terms  used  to  denote  such  things, 
and  that  at  least  one  of  them  was  interested  enough  in  these 
things  to  write  down  a  long  story  that  turns  upon  them — a 
story,  too,  that  shows  a  strong  sympathy  for  Paul,  his  hero, 
who  is  supposed  to  believe  in  them. 

In  the  example  just  given  the  method  of  causal  inquiry 
by  which  we  discovered  some  of  the  facts  behind  a  story  was 

very  crude,  and  the  results  attained,  though  per- 

More  re- 
haps   important,   were    correspondingly  meagre,    fined  meth- 

The  method  was  crude  because  it  made  use  of 

no  sources  of  information  outside  of  the  story  itself — i.e.,  it 

proceeded  wholly  from  internal  evidence — and  because  it 


374  TESTIMONY. 

took  no  account  of  the  difference  between  different  indi- 
viduals and  the  intimate  surroundings  in  which  they  are 
placed.  It  took  account  of  the  fact  that  certain  things,  such 
as  using  a  language  that  he  had  never  learned,  would  be 
impossible  for  any  individual  whatever;  but  it  did  not  take 
account  of  the  fact  that  for  this  particular  individual  there 
must  be  other  things  which  are  equally  impossible.  More- 
over, where  each  of  several  alternatives  was  possible — e.g., 
Paul's  sincerity  or  insincerity  in  the  speech  before  Agrippa 
— it  did  not  ask  which  was  the  most  probable. 

Another  thing  to  notice  about  the  conclusions  drawn  in 
the  example  is  that  most  of  them  have  nothing  whatever  to 
do  with  the  question  or  questions  which  we  probably  had 
in  mind  when  we  read  the  story.  If  we  are  trying  to  find 
out  something  about  the  character  or  real  beliefs  of  Paul,  it 
does  us  little  or  no  good  to  know  that  he  was  the  hero  of  a 
story  that  may  have  been  written  hundreds  of  years  after  his 
death  by  a  person  who  knew  nothing  about  him  but  his 
name,  and  that  the  audience  for  which  this  person  wrote 
was  supposed  to  be  interested  in  discussions  of  sin,  forgive- 
ness, and  resurrection.  Every  story  reveals  something  about 
the  person  who  tells  it,  but  it  does  not  necessarily  reveal 
anything — except  that  the  author  knew  the  name — about 
the  persons  or  events  of  whom  it  is  told. 

To  learn  anything  from  it  about  these  persons  or  events 
we  must  find  out  who  the  author  is  and  what  relation  he 
bears  (or  has  borne)  to  them.  If  he  knows  nothing  what- 
ever about  them  (except  their  names)  we  can  learn  nothing 
about  them  (except  that  their  names  were  known  in  his  time) 
from  the  story  that  he  tells,  however  plausible  it  may  be. 
If  he  has  been  in  a  position  to  know  about  them,  so  far  as 
his  external  circumstances  are  concerned,  but  is  too  preju- 
diced in  some  particular  direction  to  perceive  or  tell  the 
exact  truth,  we  may  be  able  to  find  it  from  what  he  says  if 
we  can  find  out  what  his  prejudices  were  and  make  proper 
allowance  for  them.  If  he  really  knows  the  truth  but  has 


MORE   REFINED  METHODS.  375 

such  interests  at  stake  that  he  will  not  tell  it,  we  may  get  it 
from  him  in  spite  of  all  his  efforts  if  we  only  know  what 
these  interests  really  are. 

In  such  cases  of  prejudice  or  falsehood  we  may  get  the 
truth  from  what  the  witness  says,  and  if  we  have  patience 
and  ingenuity  enough  and  if  he  talks  enough,  or  if  we  know 
enough  about  him  and  about  the  surrounding  circumstances, 
we  undoubtedly  shall.  But  in  most  cases  this  is  too  much 
to  expect,  and  our  knowledge  or  belief  that  the  witness  is 
prejudiced  or  untruthful  only  leaves  us  in  doubt  as  to  what 
the  facts  really  are.  On  the  other  hand,  if  a  witness  who  is 
in  a  position  to  know  the  facts  is  both  unprejudiced  and 
truthful,  and  if  we  know  it,  we  are  vastly  better  off.  We 
expect  him  to  make  occasional  blunders  and  so  we  cannot 
abandon  the  critical  attitude  altogether;  but  in  the  main 
our  causal  inquiry  is  greatly  simplified.  Instead  of  having 
continually  to  make  uncertain  allowances  for  some  prevail- 
ing perversity  that  may  (or  may  not)  have  affected  this,  that, 
and  the  other  statement,  we  know  that  the  vast  majority  of 
his  statements  are  substantially  true.  Any  given  one  of 
them  may  be  more  or  less  false,  to  be  sure,  and  therefore  if 
the  matter  about  which  it  is  made  has  intrinsic  importance 
enough  to  justify  the  trouble,  we  must  inquire  further  before 
we  accept  it.  But  if  the  witness  has  really  been  in  a  posi- 
tion to  know  and  if  he  is  really  truthful  and  unprejudiced, 
there  is  no  reason  why  all  his  blunders  should  lie  in  the 
same  direction ;  and  therefore  when  we  care  nothing  about 
mere  individual  details  as  such,  but  only  about  the  larger 
whole  into  which  they  are  all  combined,  we  may  accept  his 
statements  as  true  enough  on  the  whole  for  our  purposes. 
We  thus  avoid  the  continual  correction  of  details  which  is 
necessary  before  we  can  get  a  true  conception  of  the  events 
as  a  whole  from  the  story  of  one  who  is  prejudiced  or 
deliberately  untruthful.  The  wall  of  a  building  may  be 
plumb  although  every  brick  in  it  is  a  little  out  of  plumb  in 


376  TESTIMONY. 

one  direction  or  another,  but  it  will  not  be  plumb  if  all  the 
bricks  incline  in  the  same  direction. 

To  learn  anything  from  a  story  about  the  facts  of  which  it 
tells,  our  first  task,  as  we  have  just  seen,  is  to  identify  the 
Who  is  the  witness.  This  does  not  mean  merely  to  find  his 
witness?  name.  It  does  not  tell  us  anything  about  the 
truth  of  the  Iliad  to  know  that  the  author's  name  was 
Homer.  Knowing  who  the  witness  is  means  knowing  all 
that  we  possibly  can  about  his  personality,  his  interests, 
and  the  circumstances  under  which  he  gained  or  expressed 
his  ideas.  If  the  Iliad  is  a  work  of  pure  fiction  written 
centuries  after  the  siege  of  Troy,  it  may  reveal  very  much 
about  some  other  time  and  place,  but  it  can  tell  us  abso- 
lutely nothing  about  what  transpired  at  that  siege.  Many 
of  the  stories  that  we  read  and  hear  are  precisely  such  pieces 
of  fiction.  Lawyers  and  historians  know  this,  and  therefore 
when  a  person  is  about  to  give  testimony  in  a  court  the 
lawyers  begin  by  asking  his  name,  his  residence,  his  busi- 
ness, his  relations  to  the  parties  concerned,  and  so  on;  and 
careful  historians  do  not  try  to  extract  information  from  a 
writing  until  they*  have  asked  similar  questions  about  the 
author. 

In  this  matter  of  identity  we  must  not  take  too  much  for 
granted.  It  is  often  in  the  interests  of  one  individual  to 
personate  another  or  to  forge  his  signature.  The  law  recog- 
nizes this  and  guards  against  such  deceptions  as  well  as  it 
can,  not  only  by  imposing  heavy  penalties  upon  those  who 
commit  them,  but  also  by  requiring  that  deeds  be  signed  in 
the  presence  of  a  specified  number  of  witnesses  each  of  whom 
makes  oath  that  the  deed  was  signed  in  his  presence  and 
that  he  knows  the  persons  who  signed  it.  On  the  same 
principle,  bankers  require  the  identification  of  those  who 
present  checks  for  payment;  society  demands  the  proper 
introduction  of  all  newcomers;  and  manufacturers  are  con- 
tinually warning  their  customers  against  '  spurious  imita- 
tions '.  Where  there  are  no  penalties  for  deception  and 


WHO   IS    THE   WITNESS?  377 

where  no  precautions  against  it  were  taken  beforehand  the 
need  for  caution  is  especially  great.  The  historian  in  par- 
ticular should  realize  that  the  writings  with  which  he  has  to 
deal  often  bear  the  names  of  some  one  who  did  not  write 
them;  for  it  is  easy  to  ascribe  manuscripts  and  works  of  art 
of  unknown  origin  to  some  famous  maker,  just  as  it  is  easy 
to  say  that  our  rugs  were  made  in  the  Orient  or  that  our 
furniture  and  our  ancestors  '  came  over  in  the  Mayflower'. 
It  increases  their  value,  and  our  friends  are  not  usually  very 
critical  about  such  matters.  But  that  does  not  make  such 
happy  fictions  true.  The  older  any  manuscript  or  other 
possession  appears  to  be,  the  greater  is  the  danger  that  it 
has  been  assigned  to  the  wrong  person. 

One  of  the  most  famous  examples  of  false  authorship  is  the 
"Donation  of  Constantine  ".  This  remarkable  document 
purporting  to  come  from  the  early  part  of  the  fourth  century 
was  fabricated  some  time  between  750  and  840,  and  imposed 
upon  the  world  for  six  hundred  years.  In  the  document 
Constantine  is  made  to  tell  how  he  was  miraculously  cured 
of  leprosy  by  Silvester,  the  Bishop  of  Rome,  and  then  to 
hand  over  his  "  palace,  the  city  of  Rome,  and  all  the 
provinces,  places,  and  cities  of  Italy  and  [sive]  the  western 
regions  to  the  most  blessed  Pontiff  and  universal  Pope, 
Silvester  .  .  .  and  his  successors  ".  But  the  whole  style  of 
the  document  is  that  of  the  eighth  or  ninth  century,  not  of 
the  fourth;  Constantine  is  made  to  describe  himself  as  con- 
queror of  the  Huns,  though  they  did  not  appear  in  Europe 
until  at  least  fifty  years  later;  Silvester  is  described  as 
Summus  Pontifex,  though  '  this  title  was  still  borne  by  the 
chief  of  the  pagan  college  of  priests';  the  date  written  in 
the  document  is  impossible,  for  no  such  joint  consulate  as 
that  mentioned  ever  existed;  and  there  are  many  other  evi- 
dences in  the  document  itself  that  it  could  not  possibly  have 
been  written  in  the  time  of  Constantine.* 

*  I  have  used  part  of  the  translation  and  criticism  by  Thomas  Hodg- 
kin  :  "Italy  and  her  Invaders  ",  Vol.  VII,  pp.  149  ft. 


TESTIMONY. 

In  seeking  the  authorship  of  a  writing  we  cannot  even 
take  for  granted  that  the  whole  piece  was  the  work  of  a 
joint  single  author.  Sometimes  a  report  which  some 

authorship.     official  signs  is  reaily  the  work  of  half-a-dozen 

different  secretaries  or  departmental  managers.  Sometimes 
the  principal  author  had  a  collaborator  whose  name  does 
not  appear.  Sometimes,  again,  the  original  piece  has  been 
garbled  by  a  copyist  or  an  editor  or  a  whole  series  of  them, 
each  one  of  \\hom  made  some  stupid  blunder  or  tried  to 
improve  the  story. 

We  cannot  detect  the  work  of  different  authors  and  editors 
in  the  same  piece  unless  we  assume  that  human  beings  are 
subject  to  the  general  uniformity  of  Nature,  and  that  there- 
fore a  person's  vocabulary,  style,  knowledge,  and  interests 
do  not  change  suddenly  or  without  some  adequate  cause. 
To  give  an  example.  The  play  Henry  VIII.  was  assigned 
by  the  editors  who  first  published  it  to  Shakspere;  but  re- 
cent critics  tend  to  divide  it  between  Shakspere  and  Fletcher. 
The  evidence  for  the  division  that  they  make  is  found  partly 
in  the  form  of  the  verse.  Fletcher  was  very  fond  of  lines 
ending  with  an  extra,  unaccented  syllable;  Shakspere  was 
not.  Fletcher  generally  made  his  phrases  and  sentences 
end  at  the  end  of  a  line;  Shakspere  not  so  often.  Quite 
recently  Professor  Ashley  Thorndike  has  discovered  another 
test  by  which  he  confirms  the  division  made  on  such  grounds 
as  these.  He  has  noticed  that,  in  the  works  about  whose 
authorship  there  is  no  doubt,  Fletcher  almost  always  con- 
tracts the  word  '  them  '  to  '  'em  ',  using  the  latter  fourteen 
or  fifteen  times  as  often  as  he  uses  the  former,  while  Shak- 
spere uses  '  'em  '  rarely  and  '  them  '  frequently;  and  he  finds 
that  the  use  of  these  words  in  each  part  of  the  play  agrees 
with  that  of  the  author  to  whom  the  part  is  assigned.* 

A  more  complex  example  of  the  method  by  which  a 
document  is  shown  to  be  the  work  of  several  different 

*  "The  Influence  of  Beaumont  and  Fletcher  on  Shakspere",  O.  B. 
Wood,  Worcester,  Mass.,  1901. 


JOINT   AUTHORSHIP.  379 

authors  and  by  which  his  own  part  is  assigned  to  each  is 
found  in  recent  researches  into  the  origin  of  the  first  six 
books  of  the  Bible.  According  to  the  critics,  or  some  of 
them,  the  composite  character  of  these  books  is  proved  by 
such  facts  as  these:  (A)  The  "many  unnecessary  repeti- 
tions" which  they  contain,  e.g.,  the  creation  of  beasts  and 
birds  in  Genesis  i.  21-25,  and  again  in  ii.  19,  and  of  man 
in  i.  27  and  ii.  7;  the  story  of  the  Manna  and  the  quails  in 
Ex.  xvi  and  again  in  Nu.  xi ;  and  the  frequent  repetition 
of  similar  laws  in  the  legislative  portions  of  the  books. 
(B)  "Frequent  discrepancies  and  inconsistencies",  e.g. , 
the  account  of  creation  in  Gen.  ii.  ^b  and  i.  i  to  ii.  4^; 
different  statements  as  to  the  duration  of  the  flood;  Abra- 
ham's incredulity  about  the  birth  of  a  son,  Isaac,  on  account 
of  his  own  advanced  age,  and  yet  his  subsequent  marriage 
after  Sarai's  death;  the  law  that  altars  shall  be  of  unhewn 
stone,  unpolluted  by  the  use  of  any  tool  upon  them  (Ex. 
xx.  24),  and  the  directions  for  ornamenting  an  altar  of  acacia- 
wood  (Ex.  xxvii.  1-8).  (C)  "  The  want  of  continuity  and 
order  in  the  narratives,  e.g. ,  in  the  stories  of  Abraham,  Noah, 
and  Lot.  The  story  as  it  stands  in  Ex.  xix  makes  Moses, 
an  old  man  of  eighty,  ascend  and  descend  the  mountain  more 
than  four  times.  (D)  The  "differences  in  style  and  con- 
ception ".  According  to  the  first  chapter  of  Genesis  man 
and  woman  are  made  together,  apparently  out  of  nothing,  at 
the  end  of  creation.  According  to  the  second,  Adam  is  made 
first  out  of  the  dust  of  the  earth  and  Eve  is  made  last  out 
of  his  rib,  when  no  helpmeet  for  him  could  be  found  among 
the  brutes  who  were  created  in  the  meantime.  "  The  first 
account  is  in  form  artificial  and  rhythmical,  and  the  second 
graphic  and  picturesque." 

So  much  for  the  kind  of  evidence  by  which  critics  believe 
it  can  be  proved  that  these  books  are  not  all  the  work  of  the 
same  author. 

When  it  comes  to  the  identification  of  the  different  authors 
whose  work  has  been  combined,  it  is  necessary  to  study  the 


380  TESTIMONY. 

documents  much  more  closely.  Throughout  almost  all  of 
Leviticus  and  Numbers  the  writing  is  characterized  by  a 
'  love  of  ceremonial  law,  fondness  for  statistical  details, 
tendency  to  symmetry  and  similarity  of  phraseology,  the 
insertion  of  the  same  or  similar  headings,  and  a  style  that 
in  general  is  stiff  and  formal.  When  narratives  occur  they 
are  little  more  than  a  collection  of  dry  annals  '.  Moreover, 
the  language  of  the  original  Hebrew  shows  certain  pecu- 
liarities and  uniformities.  Since  passages  with  these  same 
peculiarities  are  found  scattered  throughout  other  parts  of 
the  Hexateuch  they  are  all  assigned  to  the  same  writer  or 
group  of  writers,  called  P  on  account  of  his  priestly  ten- 
dencies. Since  some  of  these  passages  written  by  P  refer  to 
what  could  not  possibly  have  existed  before  the  centraliza- 
tion of  worship  in  the  time  of  Solomon's  temple,  critics 
assume  that  they  could  not  have  been  written  before  the 
building  of  that  temple;  and  the  relative  maturity  of  many 
of  the  conceptions  points  to  a  much  later  date.  From  the 
minute  directions  as  to  the  order  and  ceremony  of  worship 
critics  infer  further  that  P  wrote  at  a  time  when  such  direc- 
tions were  necessary — probably  when  worship  in  the  temple 
had  been  interrupted  by  a  period  of  exile — and  so  they  infer 
that  P's  work  is  probably  "  the  result  of  the  religious  move- 
ment which  began  with  Ezekiel  in  Babylon  and  found  its 
completion  with  Ezra  ". 

The  Book  of  Deuteronomy  is  as  marked  in  its  character- 
istics as  Numbers  and  Leviticus,  but  very  different.  Its 
style  is  '  smooth  and  flowing,  redundant,  pleasant  to  the  ear, 
but  sometimes  tedious  from  the  accumulation  of  synonyms  '. 
Its  aim  is  monotheistic  and  its  character  hortatory.  It  is 
remarkable  for  "  its  tone  of  gentle  pleading,  its  spirituality 
as  regards  both  God  and  man.  God  has  no  outward  and 
visible  form;  God  is  near  man,  and  His  law  within  man's 
heart  ".  It  is  "  the  Gospel  of  the  Hexateuch  ".  From  the 
presence  of  these  and  other  characteristics  so  different  from 
those  of  P,  critics  infer  that  Deuteronomy  was  written  by 


JOINT   AUTHORSHIP.  381 

another  author,  D;  and  they  attribute  to  him  or  to  others 
of  his  time  and  spirit  the  other  passages  scattered  throughout 
the  Hexateuch  which  are  marked  by  the  same  peculiarities. 
Since  D  refers  to  the  monarchy,  the  prophetic  order  and  the 
priesthood  of  the  Levites,  it  is  inferred  that  this  writer  or 
group  of  writers  could  not  have  lived  and  written  before 
these  institutions  were  established.  From  the  similarity 
between  the  spirit  of  D  and  that  of  the  prophetic  movement 
in  the  reign  of  Josiah  and  from  other  evidence  it  is  inferred 
that  Deuteronomy  or  some  of  it  is  the  book  of  the  law  dis- 
covered in  that  reign,  and  written  not  many  years  earlier  by 
some  one  who  shared  in  the  prophetic  movement. 

When  the  writings  of  P  and  D  are  removed  other  passages 
still  remain,  and  these  seem  to  have  been  written  at  an 
earlier  period.  The  institutions  to  which  they  refer  are  more 
primitive,  and  the  language  seems  like  that  of  one  who  is 
thoroughly  familiar  with  them.  These  passages  are  supposed 
to  constitute  or  to  be  taken  from  the  old  book  of  the 
Covenant,  and  are  therefore  denoted  by  the  letter  C;  but 
when  they  are  examined  closely  it  is  seen  that  they  are  not 
all  alike,  and  the  differences  between  them  and  the  way  in 
which  they  are  combined  seem  to  show  that  they  are  the 
blended  product  of  at  least  two  different  writers  in  different 
periods. 

In  one  set  of  these  remaining  passages  the  name  Jehovah 
(translated  The  LORD  in  our  English  Bible)  is  almost  always 
used  for  God ;  and  God  is  given  very  human  characteristics : 
He  makes  Adam  out  of  the  dust,  walks  with  him  in  the 
cool  of  the  evening,  sends  confusion  of  tongues  to  prevent 
the  human  race  from  becoming  too  strong,  and  has  to  go 
down  to  Sodom  to  find  out  what  is  taking  place  there.  In 
this  same  set  of  passages  the  name  Israel  is  used  for  Jacob, 
and  Sinai  for  Horeb,  Israel  and  other  names  are  used  col- 
lectively to  denote  the  Sons  of  Israel  and  of  other  tribal 
ancestors,  and  there  are  certain  peculiar  phrases,  such  as 
"  to  call  upon  the  name  of  Jehovah  ".  In  these  passages, 


382  TESTIMONY. 

too,  the  narratives  are  always  vivid  and  interesting  and  the 
conceptions  are  very  naive.  Miracles,  for  example,  are 
recorded  without  any  insistence  upon  their  miraculous  char- 
acter, as  though  they  were  perfectly  natural.  These 
passages  are  therefore  assigned  to  one  writer,  or  group  of 
writers,  known  from  his  name  for  God  as  J.  In  the  other 
set  of  passages  in  C  the  name  Elohim  (translated  God)  is 
used  instead  of  Jehovah,  unless  there  is  some  special  reason 
for  using  the  latter;  and  God  is  conceived  of  as  more  separate 
from  man  than  in  the  passages  assigned  to  J,  and  not  so 
human.  Amorites  are  spoken  of  instead  of  Canaanites, 
Horeb  instead  of  Sinai,  Jacob  instead  of  Israel  (though  not 
always),  the  word  '  lord  '  is  used  to  mean  husband,  and 
there  are  other  linguistic  peculiarities.  The  style  is  more 
stiff  and  formal  than  J's  and  not  so  interesting,  and  the 
general  conception  of  things  is  more  sophisticated.  When 
miracles  are  mentioned,  for  example,  their  miraculous  char- 
acter is  recognized  and  perhaps  insisted  upon.  This  second 
set  of  passages  is  therefore  assigned  like  the  first  to  a  single 
author  or  group  of  authors,  E.  The  greater  naivete  of  the 
conceptions  expressed  by  J  indicate  that  he  was  an  older 
writer  than  E,  though  the  stories  told  by  each  of  them 
probably  originated  at  different  dates,  and  some  "  were  per- 
haps centuries  old  ".* 

For  historical  purposes  it  is  often  much  more  essential  to 
distinguish  the  work  of  a  given  author  from  that  of  his 
editors  than  from  that  of  his  collaborators,  for  the  latter  at 
least  were  his  contemporaries;  and  even  though  their  state- 
ments may  not  be  so  trustworthy  as  those  of  the  author 
himself,  the  ideas  which  they  express  and  the  words  in  which 
they  express  them  must  have  existed  in  the  author's  time 

*  See  Article  Hexateuch,  in  the  "  Dictionary  of  the  Bible  ",  published 
by  T.  &  T.  Clark  in  iSfjo.  The  account  of  Hexateuchal  analysis  which 
I  have  given  in  the  text  is,  I  hope,  sufficient  to  give  some  idea  of  the 
method  involved  in  such  investigations.  It  is  far  too  fragmentary  and 
superficial  to  be  accepted  as  an  accurate  account  of  their  results. 


JOINT   AUTHORSHIP.  383 

and  country.  If 'we  are  fortunate  enough  to  possess  several 
different  manuscripts  which  have  descended  through  different 
editors  from  the  same  original,  the  agreements  and  differences 
between  them  will  make  it  relatively  easy  to  '  restore  '  the 
original,  or  find  what  it  really  did  (and  did  not)  contain. 
If  there  is  only  one  text,  the  task  is  harder,  for  we  must 
depend  altogether  upon  the  same  kind  of  data  as  those 
which  must  be  used  for  the  discovery  of  collaborators.  But 
however  difficult  this  work  of  restoration  may  be,  it  cannot 
be  dispensed  with  if  we  wish  to  prove  anything  by  the  writ- 
ing in  question;  for  a  subsequent  addition  to  a  book  proves 
nothing  about  the  times  in  which  the  book  itself  was  written, 
and  the  firmest  possible  faith  in  a  given  individual  gives  no 
ground  for  believing  something  that  he  never  said.  A 
writing  whose  authorship  has  been  determined  is  said  to  be 
'  authentic  '.  But  this  word  does  not  imply  anything  about 
the  truth  of  the  statements  that  it  contains. 

When  the  witness  is  identified,  the  author  found,  his  text 
restored,  what  then  ?  If  he  has  not  been  in  a  position  to 
know  anything  whatever  about  the  events  of  which  he 
speaks,  except  perhaps  a  few  names — that  is  to  say,  if  his 
conceptions  have  not  been  caused  in  any  way  by  these 
events — it  may  be  worth  while  to  account  for  his  knowledge 
of  the  names,  but  otherwise  we  can  learn  nothing  from  him. 
If,  on  the  other  hand,  he  has  been  in  a  position  to  know 
about  the  events  of  which  he  speaks — if  his  story  is  in  some 
way  or  other  the  result  of  an  impression  made  upon  him  by 
these  events — we  must  examine  his  account  of  them  in  the 
light  of  all  that  we  can  find  out  about  the  witness  himself, 
his  circumstances,  the  interests  he  had  at  stake,  his  preju- 
dices and  his  veracity,  and  thus  try  to  discover  the  events 
themselves  by  finding  the  cause  that  would  be  most  likely  to 
produce  the  story  that  he  tells. 

First  the  question  of  how  the  witness  got  his  information. 
Witnesses  do  not  as  a  rule  discuss  this  question  •  they  simply 
speak  with  an  air  of  authority  which  leads  the  unsuspecting 


384  TESTIMONY. 

hearer  to  assume  that  they  know.  If  they  do  mention 
How  does  their  sources  of  information,  they  generally  make 
he  know  ?  them  appear  better  than  they  really  are.  A  per- 
son may  describe  himself,  for  example,  as  an  '  eye-witness  ' 
of  some  great  battle  in  which  he  took  part.  But  a  battle  is 
much  too  large  and  complex  an  affair  for  any  single  individual 
to  see  the  whole  of  it,  much  less  one  who  is  busy  fighting  in 
his  own  part  of  the  field.  Nine-tenths  or  more  of  what  the 
'eye-witness'  probably  tells  about  is  therefore  based  upon 
conjecture  or  the  confused  tales  of  other  combatants  often 
heard  at  fourth  or  fifth  hand. 

If  a  witness  got  his  information  through  somebody  else  and 
if  he  is  not  himself  a  trained  investigator,  his  statements  must 

be  taken  with  the  greatest  caution.  This  second- 
Hearsay. 

hand  evidence,  or  "evidence  which  does  not  de- 
rive its  value  solely  from  the  credit  to  be  given  to  the  witness 
himself,  but  rests  also,  in  part,  on  the  veracity  and  compe- 
tency of  some  other  person  ",  is  what  is  known  to  the  law  as 
'  Hearsay  ';  and  except  in  a  few  specified  classes  of  cases  our 
courts  refuse  even  to  listen  to  it.  "The  law  requires  .  .  . 
the  testimony  of  those  who  can  speak  from  their  own  per- 
sonal knowledge.  It  is  not  requisite  that  the  witness  should 
have  personal  knowledge  of  the  main  fact  in  controversy  ; 
for  this  may  not  be  provable  by  direct  testimony,  but  only  by 
inference  from  other  facts  shown  to  exist.  But  it  is  requisite 
that,  whatever  facts  the  witness  may  speak  to,  he  should  be 
confined  to  those  lying  in  his  own  knowledge,  whether  they 
"be  things  said  or  done,  and  should  not  testify  from  informa- 
tion given  by  others,  however  worthy  of  credit  they  may  be.' ' 
We  do  not  reject  hearsay  altogether  in  common  life,  and 
there  is  no  reason  why  we  should.  The  courts  can  afford  to 
•do  so  because  they  give  power  to  the  litigants  to  compel  the 
attendance  of  witnesses  (if  they  are  alive  and  within  the 
court's  jurisdiction)  who  can  speak  from  their  own  personal 
knowledge.  Moreover,  in  the  courts  the  only  matters  which 
have  to  he  proved  by  witnesses  are  those  which  one  party  or 


HOW  DOES  HE  KNOW?  385 

other  is  not  prepared  to  admit.  Thus  the  procedure  of  the 
courts  does  not  imply  that  nothing  can  be  proved  by  hearsay 
outside  of  them.  It  does  show,  however,  that  in  the  opinion 
of  jurists  hearsay  is  not  in  general  a  very  satisfactory  kind  of 
evidence.  The  objections  to  it  are  the  probability  that  the 
statement  of  the  person  quoted  ''was  imperfectly  heard,  or 
was  misunderstood,  or  is  not  accurately  remembered,  or  has 
been  perverted";  the  ease  with  which  a  lying  witness  can 
shield  himself  when  he  says  '  he  was  told  ';  the  impossibility 
of  cross-examining  the  person  quoted,  "that  it  may  appear 
what  were  his  powers  of  perception,  his  opportunities  for  ob- 
servation, hisattentiveness  in  observing,  the  strength  of  his 
recollection,  and  his  disposition  to  speak  the  truth";  and 
the  frequent  impossibility  of  telling  "through  whom,  or  how 
many  persons,  the  narrative  has  been  transmitted,  from  the 
original  witness  of  the  fact."  * 

If  we  cannot  tell  anything  about  the  origin  and  history 
of  a  story,  if  we  have  no  reason  to  believe  that  the  person  who 
tells  it  to  us  would  sift  it  thoroughly  before  telling  it,  and  if 
it  does  not  bear  some  very  strong  internal  evidence  of  truth, 

*  Greenleaf,  "  The  Law  of  Evidence  ",  §§98,  99.  The  rule  against 
the  admission  of  hearsay  does  not  of  course  exclude  everything  that  a 
witness  claims  to  have  heard  said.  Evidence  about  the  statements  of 
another  person  is  not  hearsay  when  "  the  very  fact  in  controversy  is 
whether  such  things  ivere  •written  or  spoken,  and  not  whether  they  -were 
true  ".  If  a  person  is  being  tried  for  slander  a  witness  would  be  allowed 
to  testify  that  he  heard  him  say  the  slanderous  words  ;  but  he  would  not 
be  allowed  to  testify  that  some  one  else  had  told  him  that  he  had  heard 
him  say  them.  Again,  evidence  is  not  hearsay  when  the  statements, 
whether  written  or  spoken,  which  the  witness  repeats  are  "  natural  or 
inseparable  concomitants  of  the  principal  fact  in  controversy  ".  In  a 
murder  trial,  for  example,  a  witness  may  testify  that  he  heard  the 
prisoner  threaten  to  kill  the  deceased,  not  because  there  was  necessarily 
any  truth  in  the  threat,  but  because  it  indicates  a  state  of  mind  in  which 
such  a  deed  might  be  done.  The  threat  is  thus  a  part  of  the  res  gestti ; 
it  has,  or  may  have,  a.  direct  or  indirect  causal  connection  with  the  act 
in  question;  and  it  is  thus  so  much  circumstantial  evidence,  not  hear- 
say. 


386  TESTIMONY. 

we  have  no  right  to  assume  that  it  is  true.  This  statement 
applies  to  the  ordinary  newspaper  anecdotes  about  public 
men,  to  much  of  the  gossip  that  \ve  hear  about  our  neighbors, 
and  to  almost  all  of  the  legends  of  ancient  heroes  and  medi- 
aeval saints. 

Now  comes  the  question  whether  a  witness  is  truthful.  If 
we  are  really  weighing  testimony,  this  question  must  be 
Is  he  truth-  answered  according  to  some  rational  principle. 
To  depend  upon  our  impulses  for  an  answer  is 
not  to  weigh  it  at  all,  but  merely  to  return  to  the  primitive 
condition  in  which  we  were  before  we  discovered  the  need 
for  weighing  it.  Hence  we  must  not  assume  that  a  witness 
is  truthful  merely  because  the  story  he  tells  is  pleasant  or  flat- 
tering, or  because  it  is  interesting  or  pathetic  ;  because  he  is 
polite  or  intelligent,  his  voice  and  accent  winning,  or  his 
manner  confidential ;  because  he  was  hard  to  find,  knows  so 
much  about  the  subject,  or  is  perhaps  the  only  person  whom 
•we  can  find  that  knows  anything  about  it  at  all.  We  must 
not  trust  him  either  merely  because  he  was  doubted  once  be- 
fore and  vindicated,  or  even  because  '  he  told  us  himself  he 
that  was  telling  the  truth  ' .  So,  vice  versa,  we  must  not  assume 
that  a  witness  is  untruthful  or  ignore  what  he  says  merely 
because  he  is  uninteresting  or  disagreeable. 

In  the  effort  to  escape  the  influence  of  our  impulses  where 
impulses  are  liable  to  mislead,  and  to  find  some  fixed  test 
Arbitrary  of  veracity,  there  is  danger  of  choosing  something 
purely  arbitrary  ;  of  assuming,  for  example,  that 
there  must  always  be  '  truth  on  both  sides '  when  witnesses 
disagree,  and  trying  to  split  the  difference  between  them  ;  or 
of  assuming  that  the  story  supported  by  the  larger  number  of 
witnesses  must  be  the  true  one,  regardless  of  the  character  of 
the  individual  witnesses  and  their  sources  of  information. 

Because  truthfulness  is  right  and  lying  wrong,  people  have 
often  invented  arbitrary  tests  based  upon  the  supposition  that 
God  would  intervene  in  some  particular  manner  to  vindicate 
the  right  and  punish  the  wrong.  Thus  a  person  sometimes 


IS   HE   TRUTHFUL?  387 

says,  '  May  God  strike  me  dead  if  what  I  say  is  not  true  ',  and 
in  a  case  of  this  sort  if  the  calamity  named  does  happen  to 
occur  it  is  often  accepted  by  those  who  see  it  as  a  divine 
judgment.  Such  tests  are  easily  systematized  and  adopted 
by  a  people  as  a  whole.  Consequently  the  Hebrews  cast  lots 
to  discover  a  culprit,  and  our  own  ancestors  in  the  middle  ages 
appealed  to  the  ordeal  or  to  trial  by  combat.  Such  tests  still 
survive,  although  the  definite  appeal  to  God  may  be  lost ; 
and  schoolboys  assume  that  one  of  their  number  has  '  de- 
fended his  word  '  or  proved  his  truthfulness  if  he  has  won  a 
fight  with  the  boy  who  impeached  it.  In  the  same  way  when 
boys  play  the  disputed  part  of  some  game  over  again,  the 
winner  announces  that  'that  proves  it '. 

If  such  simple  methods  as  these  for  settling  the  rights  of 
a  case  and  the  veracity  of  the  witnesses  had  been  found 
effective,  the  state  and  the  church  would  certainly  still  con- 
tinue to  use  them.  Nowadays,  however,  we  recognize  that 
God  or  Nature  gives  no  arbitrary  sign  by  which  we  can  detect 
a  lie  and  vindicate  the  truth.  We  are  not  left  wholly  without 
a  test — far  from  it ;  but  the  test  which  we  have  is  hard  to 
apply  and,  like  the  oracles  of  old,  it  often  leaves  us  in  doubt. 
There  is  no  ultimate  test  of  truthfulness  but  fact,  and  the  test 
of  fact  is  nothing  less  than  consistency  with  the  whole 
course  of  Nature. 

When  the  fact  itself  is  unknown  and  we  are  trying  to  esti- 
mate a  witness's  veracity  in  order  to  find  it,  the  most  im- 
portant things  to  consider  are  his  personality  ;  his  special 
relations  to  the  question  about  which  he  speaks ;  the  consis- 
tency and  probability  of  the  story  he  tells;  and  its  relations 
to  the  stories  of  other  witnesses.  We  must  speak  of  each. 

First  the  witness  himself.  We  must  not  judge  everybody 
by  ourselves.  Whether  a  person  has  a  strong  disposition  to 
speak  the  truth  is  largely  a  matter  of  his  own  in- 

,..,,,  m     •        •  i  •  rr  i  •  r 

dividual  character.      I  his  is  very  different  in  dif- 
ferent people,  and  it  is  something  about  which  we  cannot 
always  know.     We  often  can  know,  however,  about  a  per- 


388  TESTIMONY. 

son's  race,  the  age  in  which  he  lived,  his  occupation,  and  the 
set  to  which  he  belonged ;  and  all  these  help  to  determine 
his  veracity.  An  Oriental  is  generally  less  likely  to  speak 
the  truth  than  a  European,  a  slave  than  a  master,  a  promoter 
than  a  military  officer.  If  Othello  had  stopped  to  think,  he 
might  have  known  that  an  Italian  of  lago's  time,  even 
though  an  officer,  would  not  hesitate  to  deceive  a  man  of 
alien  race  if  he  had  anything  to  gain  by  it. 

In  considering  the  effects  of  character  we  must  not  assume 
that  the  most  innocent  persons  are  necessarily  the  most 
truthful.  A  child  may  tell  the  most  harmful  lies  in  all  inno- 
cence simply  because  the  thought  has  come  (or  been  put) 
into  its  head,  and  he  has  not  critical  judgment  enough  to 
distinguish  clearly  between  truth  and  falsehood  or  to  recog- 
nize the  vvrongness  of  the  latter.  A  child  once  more  may  lie 
from  pure  nervousness.  Ask  him  in  a  threatening  tone 
whether  he  has  done  some  perfectly  innocent  thing  which 
you  have  seen  him  doing,  and  very  likely  he  will  deny  it. 

Next  the  circumstances.  We  must  not  divide  people  once 
for  all  into  sheep  and  goats,  those  who  lie  or  prevaricate  and 
Circum-  those  who  do  not.  "  Falsus  in  uno  falsus  in 
stances.  omnibus"  does  not  mean  that  if  a  person  lies 
once  he  will  lie  always,  but  only  that  he  is  Lkely  to  lie 
again  on  the  same  occasion  and  about  the  same  matter. 
Conversely,  though  a  person  has  never  yet  told  a  lie,  he  may 
tell  one  in  some  new  situation  where  the  strain  is  greater. 
There  always  must  be  first  offences.  Therefore,  when  we 
have  estimated  a  witness's  general  character,  truthfulness 
and  characteristic  motives  as  well  as  we  can,  we  must  try  to 
find  out  what  special  circumstances  are  present  to  influence 
him.  Much  depends,  for  example,  upon  the  solemnity  of 
the  occasion  on  which  the  statement  is  made.  A  person  is 
not.  likely  to  lie  when  he  is  confessing  to  his  priest  or  when 
he  knows  he  is  at  the  point  of  death.  The  law  recognizes 
the  influence  of  this  solemnity,  and  therefore  it  demands 
that  every  witness  who  comes  into  court  shall  swear  to  tell 


INTERESTS.  389 

the  truth ;  *  but  on  the  same  principle  it  regards  a  dying 
declaration,  even  when  the  witness  was  not  sworn,  as  equiva- 
lent to  an  oath. 

One  of  the  most  important  circumstances  which  we  have 
to  consider  is  the  effect  which  the  witness  expects  his  story 

to  have  upon  his  interests.     If  the  story  which  he 

.  .  Interests. 

deliberately  tells   is  against  his  own  interests  or 

the  interests  of  those  whom  he  would  like  to  help,  and  if  he 
must  realize  this,  it  is  much  more  likely  to  be  true  than  if  it 
were  one  which  he  probably  believed  to  be  favorable  ;  for 
people  often  lie  to  further  their  interests,  but  not  to  injure 
them.  Here  again  the  law  recognizes  our  natural  tendencies 
and  attaches  great  importance  to  confessions  of  guilt  or  other 
statements  against  one's  own  interest,  while  on  the  other  hand 
it  has  generally  refused  to  listen  to  the  testimony  of  any  one 
who  has  a  pecuniary  interest  in  the  result  of  a  suit  or  to  a 
prisoner  who  is  on  trial,  regarding  the  latter' s  plea  of  '  not 
guilty '  as  a  plea  only,  or  a  demand  that  the  charge  be 
proved,  and  not  as  evidence. f 

While  we  may  learn  something  from  the  procedure  of  the 
courts,  we  must  be  careful  in  this  case,  as  in  that  of  hearsay, 
not  to  infer  too  much  from  it.  A  court  of  law  cannot  admin- 
ister justice  effectively  (especially  when  the  work  is  divided 


*  The  oath  is  intended  to  direct  the  attention  of  the  witness  to  God — 
not  to  direct  the  attention  of  God  to  the  witness. 

•j-  Dying  declarations  and  statements  against  interest,  including  con- 
fessions of  guilt,  are  two  of  the  very  few  kinds  of  hearsay  that  the  law 
admits  as  evidence.  Of  course  the  witness  who  tells  of  a  person's  ad- 
missions or  confessions  must  have  heard  them  himself  and  not  merely 
heard  some  third  person  tell  about  them. 

The  refusal  to  listen  to  an  accused  person  is  partly  in  his  own  interest. 
His  testimony  cannot  help  him  very  much  in  any  case,  for  he  would  not 
be  on  trial  if  his  word  were  not  suspected  ;  and  if  he  is  really  innocent, 
it  may  do  him  much  harm,  on  account  of  the  embarrassing  circum- 
stances under  which  it  is  given.  Hence  in  States  where  the  prisoner  is 
allowed  to  speak  in  his  own  defence  the  jury  is  warned  that  if  he  does 
not  choose  to  do  so,  it  must  not  be  taken  as  any  evidence  of  guilt. 


39°  TESTIMONY. 

as  it  is  in  our  system  between  a  judge  and  a  jury)  unless  it 
acts  according  to  general  rules ;  and  evidence  which  the  rule 
excludes  might  sometimes  be  recognized  as  perfectly  good  if 
it  could  be  considered  on  its  individual  merits.  Again,  as 
we  said  concerning  hearsay,  the  questions  of  fact  that  juries 
have  to  settle  are  always  disputed ;  and  rules  which  may  be 
perfectly  appropriate  in  settling  disputes  that  the  disputants 
cannot  settle  for  themselves  maybe  quite  absurd  when  applied 
to  matters  that  were  never  disputed.  Then,  too,  it  must  be 
remembered  that  a  person  is  not  usually  brought  to  trial  for 
an  alleged  crime  unless  there  is  at  least  some  prima  facie 
evidence  against  him,  and  that  in  every  civil  suit  that  turns 
on  some  question  of  fact,  one  of  the  two  litigants  must  have 
a  bad  case  and  be  trying  wittingly  or  unwittingly  to  'make 
the  worse  appear  the  better  reason.'  When  both  parties  to 
a  transaction  are  clear-headed  and  honest  they  are  not  likely 
to  get  into  court  about  it.  Even  where  misunderstandings 
arise  people  generally  succeed  in  keeping  out  of  court  when 
they  have  confidence  in  each  other's  honesty  and  fair-mind- 
edness. Under  these  circumstances  it  is  not  unreasonable 
that  the  court  should  say  :  Often  half  of  the  parties  interested 
cannot  be  trusted  ;  the  jury — untrained  as  they  are — cannot 
always  tell  from  the  way  in  which  the  parties  give  their  evi- 
dence which  half  this  is;  we  will  therefore  exclude  the  tes- 
timony of  them  all,  and  depend  upon  that  of  disinterested 
persons,  whom  we  can  nearly  always  summon,  and  whose 
average  honesty  and  intelligence  will  probably  approach 
nearer  to  that  of  the  community  as  a  whole.  This  is  very 
far  from  meaning  that  a  person  should  never  trust  his  neigh- 
bor's truthfulness  when  the  story  told  by  the  latter  happens 
to  be  in  his  own  interest. 

Though  we  need  not  always  go  so  far  as  the  courts  of  law 
and  reject  the  evidence  of  interested  parties,  we  must  not 
neglect  to  make  proper  allowance  for  their  interests.  Most 
people  who  tell  a  story,  whether  it  be  written  or  spoken, 
have  some  object  in  telling  it,  even  if  it  be  nothing  more 


INTERESTS.  391 

than  their  own  temporary  amusement  or  the  entertainment 
of  their  hearers;  and  if  the  story  is  about  some  important 
matter,  the  chances  are  that  the  narrator  has  some  personal  or 
party  interest  which  leads  him,  perhaps  insensibly,  to  distort 
the  facts  a  little  for  the  benefit  of  his  own  'side'.  If  he  is 
writing  a  biography  of  a  deceased  friend  for  circulation 
amongst  his  admirers,  it- is  moderately  certain  that  he  will 
dwell  upon  his  good  deeds  and  leave  as  many  as  he  can  of 
the  doubtful  transactions  out.  His  very  purpose  or  prejudice, 
however,  may  make  some  of  his  statements  all  the  more 
trustworthy.  If  he  mentions  a  few  '  regrettable  incidents, 
due  not  so  much  to  the  fault  of  the  deceased  as  to  the  very 
unfortunate  position  in  which  he  was  placed',  or  incidents 
for  which  he  feels  compelled  to  offer  any  other  kind  of 
apology,  his  reader  can  feel  moderately  certain  that  the  in- 
cidents occurred.  The  reader  can  be  sure  at  least  that  the 
author  believed  they  did,  and  that  he  would  probably  not 
have  believed  it  if  the  evidence  had  not  been  very  strong. 

Special  confidence  in  statements  against  the  interests  of 
those  who  make  them  is  not  deserved  unless  the  speaker 
really  knew  or  believed  that  they  were  against  his  interests. 
If  a  prisoner  had  been  told  that  '  it  would  be  better  for  him 
if  he  confessed  '  or  that  if  he  did  not  confess  he  would  be 
arrested  (and  if  he  had  not  been  subsequently  warned  that 
anything  he  said  might  be  used  against  him),  a  court  of  law 
would  refuse  to  listen  to  the  story  of  his  confession.  In  the 
same  way  the  disgusting  story  which  some  one  tells  of  his 
own  villainy  must  not  be  accepted  with  the  confidence 
which  naturally  belongs  to  a  confession  unless  it  is  disgust- 
ing to  the  narrator  as  well  as  to  the  hearer.  It  may  be  that 
he  is  really  boasting.  Again,  a  person  may  confess  some 
fault  that  he  never  committed  in  order  to  gain  sympathy  by 
the  very  fact  of  confession  or  to  show  how  good  he  is  now, 
since  he  is  willing  to  confess  it,  or  how  much  he  has  changed. 
In  a  sentimental  age  confessions  are  not  always  hurtful. 
Once  more,  if  a  man  takes  sides  against  '  his  own  country  ' 


39 2  TESTIMONY. 

and  attacks  its  leaders,  what  he  says  is  quoted  all  over  the 
world  with  the  weight  of  a  confession ;  and  yet  the  man  who 
does  it  may  have  divested  himself  of  all  special  interest  in 
his  country,  or  this  interest  may  be  outweighed  completely 
by  the  hostility  which  he  feels  towards  the  leaders  whom  he 
attacks,  or  by  the  pride  which  he  takes  in  being  thought 
'  broad-minded  '.  These  same  considerations  are  applicable 
to  the  alleged  confessions  of '  converted  '  nuns,  priests,  free- 
masons, and  pagans.  Finally,  a  confession  should  not 
carry  much  weight  unless  the  person  who  makes  it  is  in  his 
right  mind.  It  is  not  unusual  for  weak-minded  persons  to 
falsely  confess  hideous  crimes  of  which  they  have  read  or 
which  have  taken  hold  in  some  other  way  of  their  imagina- 
tion. 

The  only  direct  proof  of  a  witness's  truthfulness  or  un- 
truthfulness  in  any  particular  case  is  the  agreement  of  his 

story  with  the  facts  themselves.      We  may  reject 
Consistency     .  .     '  .  .  .     ..       .        .      .         .  . 

and  general  his  story  because  we  know  beforehand  that  his 
probability.  ,  . 

word  is  not  to  be  depended  upon;  but  we  could 

not  know  this  unless  we  had  been  able  to  compare  the  stories 
which  he  told  on  other  occasions  with  facts. 

A  story  contrary  to  fact  must  be  false,  and  unless  we  are 
willing  to  abandon  absolutely  all  tests  of  truth  and  truthful- 
ness we  must  be  prepared  to  admit  this,  no  matter  how 
trustworthy  the  author  of  the  story  may  have  previously 
seemed  to  be. 

Of  course  a  direct  comparison  with  the  facts  in  the  case  is 
impossible  when  these  are  unknown  and  it  is  through  the 
story  itself  that  we  are  trying  to  find  them.  But  there  are 
certain  more  general  facts  which  we  do  know  and  with  which 
every  true  story  must  agree.  A  story  '  inconsistent  with 
itself '  cannot  be  true  because  the  alleged  facts  which  it 
asserts  cannot  all  coexist  in  a  world  ordered  as  we  believe 
ours  to  be.  On  the  same  principle  a  story  cannot  be  true 
which  asserts  the  existence  of  any  single  state  of  affairs  which 
is  incompatible  with  the  world's  general  arrangement.  On 


CONFIRMATION   AND   CONTRADICTION.  393 

the  same  principle,  finally,  a  story  is  probably  false  if  it  is 
like  other  stories  which  often  grow  out  of  the  interests, 
prejudices,  or  vanity  of  such  narrators  as  the  witness,  under 
circumstances  like  the  present,  but  which  are  seldom  true. 
This  is  the  justification  for  incredulity  towards  tales  of 
extraordinary  luck  in  fishing,  of  wonderful  hands  in  cards, 
and  of  remarkable  coincidences  that  the  narrator  attributes 
to  occult  causes.  By  saying  that  stories  of  this  third  sort 
are  probably  false  we  do  not  mean  that  any  given  one  of 
them  is  false,  for  we  expect  the  most  improbable  of  possible 
events  to  happen  some  time  or  other.  We  only  mean  that 
a  person  who  never  believes  such  stories  in  the  absence  of 
exceptionally  strong  evidence  will  be  right  oftener  in  the 
long  run  than  one  who  generally  believes  them. 

If  there  is  any  reason  why  a  witness  should  not  wish  to 
tell  the  truth,  the  falsity  of  a  part  of  his  story  may  be  suffi- 
cient to  show  that  he  is  probably  untruthful  and  therefore  to 
discredit  all  the  rest.  But  the  falsity  of  one  part  of  a  story 
is  not  sufficient  in  itself  to  prove  the  falsity  of  the  rest.  A 
person  may  have  some  prejudice  which  prevents  him  from 
seeing  some  one  part  of  the  facts  and  yet  be  perfectly  able 
and  willing  to  tell  the  truth  about  other  parts;  or  he  may  be 
willing  to  tell  a  '  little  '  lie,  but  not  to  tell  a  '  big '  one. 
Even  when  a  witness  is  perfectly  unprejudiced  and  perfectly 
honest  a  certain  amount  of  error  and  consequent  inconsist- 
ency in  his  story  is  almost  inevitable, — so  much  so  indeed 
that  a  story  which  is  absolutely  glib  and  consistent  often 
seems  too  studied  to  be  perfectly  true. 

It  is  much  easier  to  judge  of  the  veracity  of  a  witness  if 
we  are  able  to  compare  his  story  with  that  of  others.  When 
several  independent  witnesses  agree  in  their 
stories  they  '  confirm  '  or  strengthen  each  other; 
and  the  more  of  such  witnesses  there  are  the  tlon- 
more  likely  is  the  story  to  be  true;  simply  because  each  new 
witness  makes  it  so  much  harder  to  account  for  the  agree- 
ment on  any  other  hypothesis.  We  must  be  quite  sure, 


394  TESTIMONY. 

however,  that  the  witnesses  really  are  independent.  If  they 
tell  precisely  the  same  story  in  much  the  same  words — if 
they  use  the  same  strange  phrases  or  make  the  same  im- 
probable blunders,  like  schoolboys  who  copy  each  other's 
examination-papers — it  is  practically  certain  that  they  are 
not  independent.  In  that  case  they  no  longer  confirm  each 
other:  there  is  really  only  one  story,  which  they  have  all 
learned  to  repeat.  In  matters  of  this  kind,  however,  some 
writers  of  history  are  very  careless;  for  it  is  not  at  all  un- 
common to  find  one  citing  a  whole  series  of  ancient  authors 
or  '  authorities  '  in  support  of  some  statement,  when  there 
is  not  the  slightest  doubt  that  they  all  got  the  story  from 
the  same  source. 

Discrepancies,  when  they  are  found  between  the  stones  of 
several  witnesses  who  speak  about  the  same  affair,  may  or 
may  not  indicate  that  at  least  one  of  the  witnesses  is  prob- 
ably dishonest.  If  they  do  and  if  the  witnesses  are  evidently 
working  together,  this  may  discredit  them  all;  for  a  perfectly 
honest  man  with  a  true  story  will  not  ask  or  accept  the 
assistance  of  a  dishonest  man  with  a  false  story.  But  if  there 
is  no  evidence  of  collusion  between  the  witnesses  themselves, 
the  dishonesty  of  one  ought  not  to  discredit  the  others, 
though  it  might  perhaps  discredit  the  person  who  summoned 
them  all.  It  would  be  a  gross  fallacy  to  use  Peter's  story 
(on  the  assumption  that  it  is  true)  to  discredit  Paul's  and 
then  use  Paul's  to  discredit  Peter's. 

As  we  can  judge  something  about  the  truth  or  falsity  of  a 
story  from  its  confirmation  or  contradiction  by  other  stories, 
so  likewise  can  we  often  infer  something  from  the  lack  of 
such  confirmation  or  contradiction.  The  importance  of 
some  events  is  so  great  and  their  consequences  are  so 
apparent  that,  if  they  happen  at  all,  they  are  certain  to  be 
known  by  a  vast  number  of  people  and  referred  to  in  one 
way  or  other  by  many  of  them.  If  an  alleged  event  of  this 
character  is  mentioned  by  only  one  out  of  a  large  number 
of  contemporary  writers,  it  is  a  fair  conclusion  that  he  is 


CONFIRMATION   AND   CONTRADICTION.  39$ 

romancing.  So  with  contradiction.  If  a  story  that  almost 
certainly  would  be  contradicted  if  false  is  not  contradicted, 
that  affords  some  evidence  of  its  truth.  We  must  be  careful, 
however,  not  to  rely  upon  these  tests  where  they  are  not 
applicable.  People  do  not  usually  contradict  newspaper 
anecdotes,  or  libels  that  they  think  beneath  their  notice. 
They  certainly  cannot  contradict  charges  of  which  they  are 
not  told.  Sometimes,  moreover,  a  story  is  contradicted  but 
we  do  not  hear  of  the  contradiction.  Much  the  same  is 
true,  mutatis  mutandis,  of  confirmations. 

Sometimes  the  nature  of  an  alleged  event  makes  confirma- 
tion or  contradiction  of  the  story  told  about  it  absolutely 
impossible.  If  Elijah  was  alone  at  Horeb,  as  the  story 
seems  to  imply,  a  hundred  different  documents  could  give 
no  confirmation  to  the  statements  in  I.  Kings  xix  about 
what  happened  to  him  there.  The  most  they  could  possibly 
prove  would  be  that  the  writer  in  Kings  had  correctly  stated 
Elijah's  own  account  of  it.  In  the  same  way,  a  hundred 
other  '  accounts  '  of  the  event  could  not  prove  that  Elijah's 
story  was  false,  though  they  might  prove  that  he  did  not  tell 
the  story  as  it  is  given  in  Kings. 

Before  one  story  can  confirm  or  discredit  another,  it  must 
be  clear  that  the  events  to  which  the  two  refer  are  the  same. 
This  cannot  always  be  taken  for  granted.  Because  A  and 
B  both  say  they  saw  a  woman  fall  as  she  was  getting  off  a 
street-car  in  the  city  yesterday  we  have  no  right  to  assume 
that  they  must  have  seen  the  same  accident,  for  events  of 
this  sort  are  common  enough  and  often  very  similar.  In 
the  same  way,  we  have  no  right  to  assume  without  further 
investigation  that  there  is  any  connection  between  the  story 
of  a  flood  told  by  some  tribe  of  North  American  Indians  and 
that  told  in  Genesis;  for  there  are  certain  types  of  story  that 
we  expect  to  find  everywhere — stories  of  a  creation,  of  a 
great  flood,  of  the  origin  of  speech  and  of  fire,  of  a  very 
strong  man,  a  very  wise  man,  a  very  faithful  friend  or  lover, 
of  talking  animals,  ghosts,  giants,  and  the  good  old  days. 


396  TESTIMONY. 

Such  stories  are  developed  by  a  common  mental  process  out 
of  the  common  elements  of  human  experience.  The  only 
way  to  prove  an  historical  connection  between  two  similar 
stories  of  this  sort  from  the  stories  themselves  is  to  show  that 
there  is  more  similarity  between  their  details  than  the  general 
similarity  of  human  thought  and  experience  will  account 
for.  It  is  not  remarkable  that  the  Hebrews  and  the  Greeks 
should  both  have  stories  of  a  wise  man  and  of  a  faithful 
friend ;  but  it  is  curious  that  the  names  Solomon  and  Solon, 
David  and  Damon,  should  be  so  similar,  and  a  few  more 
coincidences  of  this  sort  would  suggest  very  strongly  some 
historical  connection  between  two  sets  of  stories  or  the 
events  on  which  they  are  based. 

So  much  for  the  tests  by  which  we  judge  of  the  veracity 
of  a  witness  and  the  probable  truth  or  falseness  of  his  story. 
If  these  tests  give  us  reason  to  believe  that  he  was  in  a  posi- 
tion to  know  about  the  matters  of  which  he  speaks  and  that 
in  the  main  he  is  unprejudiced  and  truthful,  the  task  which 
remains  for  us  is  comparatively  easy.  But  if  we  have  found 
that  he  is  prejudiced  or  untruthful,  it  is  not  necessarily  hope- 
less. In  this  case  (as  in  the  other)  we  are  far  better  off  when 
we  have  the  accounts  of  several  different  witnesses  than  when 
we  have  only  that  of  one,  no  matter  how  prejudiced  or 
untruthful  we  may  believe  each  one  of  these  different  wit- 
nesses to  be,  or  how  conflicting  their  stories  are.  For  every 
lie  must  be  made  to  fit  somehow  or  other  into  a  background 
of  truth.  The  person  who  tells  it  lived  in  a  real  world  and 
he  is  bound  to  express  his  ordinary  conceptions  of  that  world 
up  to  the  point  at  which  he  thinks  it  necessary  to  falsify 
things  in  order  to  make  his  principal  lie  seem  consistent  with 
itself  and  with  admitted  facts.  Different  persons  lying 
about  the  same  event  (however  much  they  may  agree  about 
the  main  point  at  issue)  are  bound  to  connect  the  false  state 
of  affairs  which  they  allege  with  the  true  which  they  take  for 
granted,  in  different  ways;  and  if  each  of  them  is  cross- 
examined  carefully  enough,  they  will  probably  reveal  enough 


THE  JUDGE   MUST  JUDGE   IMPARTIALLY.  397 

between  them  to  make  it  perfectly  plain  what  the  truth  must 
have  been.  In  this  case,  as  in  every  other,  the  more  effects 
of  a  given  cause  we  know  the  more  likely  we  are  to  find  out 
what  the  cause  itself  really  was.  When  a  person  merely 
wishes  to  absorb  the  truth  from  others  a  contradiction 
between  them  is  necessarily  very  embarrassing;  but  when  he 
is  trying  to  find  the  cause  that  lay  back  of  their  statements 
it  may  be  very  helpful. 

To  what  has  been  said  about  the  principles  by  which  evi- 
dence should  be  weighed  I  should  like  to  add  a  few  words 
about  the  attitude  of  the  judge  who  has  to  apply  them. 

If  anybody  wishes  to  have  a  question  settled  on  its  merits, 
he  must  make  sure,  to  begin  with,  that  the  judge  or  jury  to 

which    he    submits    it    is    not    so    incompetent, 

The  judge 
dependent,    interested,    or   prejudiced   that    the   mustjudee 

investigation  will  be  a  mere  mockery.  The  State 
tries  to  provide  for  this  by  appointing  judges  who  are  learned 
in  the  law,  and  often  by  appointing  them  in  such  a  way  and 
for  such  a  period  that  they  will  be  independent  of  those 
whose  cases  they  have  to  judge  and  of  popular  whims  in 
general ;  by  refusing  to  accept  as  a  juryman  any  one  who  has 
any  personal  interest  in  the  outcome  of  a  case  or  who  has 
already  formed  an  opinion  upon  its  merits;  by  providing  that 
lawyers  shall  not  ask  '  leading  questions  ',  or  those  which 
indicate  to  the  witnesses  by  their  form  what  answer  is 
desired;  and  by  visiting  severe  penalties  upon  any  one  who 
attempts  to  'tamper'  in  any  way  with  judge,  jury,  or  wit- 
nesses. In  the  settlement  of  our  own  problems  we  must 
not  forget  to  take  similar  precautions.  If  the  question  is 
one  which  demands  special  skill  (whether  it  be  in  medicine  or 
in  morals),  we  should  choose  our  judge  with  reference  to  his 
skill,  not  with  reference  to  the  decision  that  we  think  he 
will  give.  If  we  desire  an  estimate  of  our  own  conduct,  we 
should  not  go  for  it  to  our  admirers  or  dependents,  to  those 
who  have  not  the  courage  to  form  an  opinion  of  their  own 
and  tell  us  what  it  is,  or  to  those  who  cannot  condemn  or 


398  TESTIMONY. 

approve  of  what  we  have  done  without  also  passing  judg- 
ment upon  themselves.  When  we  have  chosen  our  judge 
we  must  put  our  questions  fairly,  in  such  a  way  as  to  bring 
out  the  opinion  held  by  him,  and  not  in  such  a  way  as  to 
tempt  him  merely  to  echo  the  opinion  held  or  desired  by  us. 
We  must  not  therefore  say  to  him,  '  Isn't  this  true  ?  '  or 
'  Don't  you  think  so  ? '  and  we  must  not  beg  him  not  to  be 
'  too  unfavorable  '  or  '  too  hard  on  us  '.  When  all  that  we 
seek  is  an  opinion  it  is  absurd  to  bribe  the  judge  and  then 
congratulate  ourselves  upon  his  decision. 

When  we  ourselves  are  called  upon  to  act  as  judges  we 
must  strive  hard  to  resist  not  only  the  importunities  of  those 
According  to  who  appeal  to  us,  but  the  influence  of  our  own 
evidence.  desires  and  prejudices  as  well.  Like  good  old 
Locke  we  must  be  able  to  say  in  all  sincerity,  "  It  is  truth 
alone  I  seek";  and  we  must  be  prepared  to  judge  of  the 
truth  by  the  evidence,  not,  like  sentimentalists,  to  ignore 
the  evidence  or  discredit  or  distort  it  because  it  is  not  what 
we  should  like.  If  we  have  interests,  prejudices,  or 
cherished  beliefs  which  are  affected  by  the  issue,  we  must 
deliberately  force  them  aside  until  after  the  decision  has  been 
rendered.  We  must  not  heed  the  '  appeal  to  consequences  ', 
which  points  out  that  if  we  believe  one  thing  we  shall  be 
forced  to  believe  something  else  also  which  is  unplea-sant, 
though  not  necessarily  untrue.  If  the  affair  touches  us  and 
those  we  love  and  honor  so  deeply  that  we  cannot  cast  aside 
these  interests  and  prejudices  until  the  decision  is  given, 
then  we  must  recognize  that  so  far  as  this  question  is  con- 
cerned we  are  not  proper  judges,  and  leave  the  decision  to 
some  one  else. 

Again,  when  we  ourselves  have  been  called  upon  to  decide 
a  case  (whether  it  be  to  determine  some  fact  itself  or  to  dis- 
cover what  authority  is  best  fitted  to  determine 
Mnst  judge  jt^  we  must  not  forget  that  for  the  moment  at 
least  we  have  assumed  a  position  of  independ- 
ence, and  we  have  no  right  to  quietly  abandon  this  position 


MUST  JUDGE   FOR   HIMSELF.  399 

until  our  task  is  finished  or  definitely  given  up.  The 
decision  which  we  reach  must  be  based  upon  facts,  and  the 
burden  of  drawing  the  inference  from  the  facts  rests  upon 
us  and  not  upon  anybody  else.  To  find  the  facts  from 
which  an  inference  can  be  drawn  it  is  our  right  and  our  duty 
to  get  all  the  testimony  we  can;  but  when  a  witness  has 
given  us  all  the  facts  that  he  knows  we  have  no  right  to  ask 
what  inference  he  draws  from  them,  and  then  merely  absorb 
his  opinions,  any  more  than  a  lawyer  has  the  right  to  ask  a 
witness  whether  he  believes  the  prisoner  is  guilty  instead  of 
merely  asking  him  what  he  saw  the  prisoner  do,  and  leaving 
the  question  of  guilt  to  the  jury.  If  it  is  we  who  are  called 
upon  to  decide,  even  an  expert  cannot  relieve  us  of  our 
responsibility.  A  lawyer  has  a  right  to  ask  an  expert  on 
gunshot  wounds  how  far  the  muzzle  of  a  gun  must  have  been 
from  the  body  of  the  deceased  when  he  was  shot ;  but  he 
has  no  right  to  ask  whether  the  witness  believes  that  the 
prisoner  killed  him.  This  is  the  question  which  the  jury 
must  settle — and  settle  for  itself.  So,  likewise,  if  you  happen 
to  be  a  director  in  a  company,  it  is  your  business  to  ex- 
amine the  accounts  yourself  and  see  that  everything  is  right. 
If  there  is  anything  which  you  do  not  understand,  you 
must  insist  upon  having  it  explained,  not  merely  to  the 
limit  of  the  manager's  patience,  but  to  your  own  full  satis- 
faction. It  is  your  business  to  judge  for  yourself,  and  you 
are  not  doing  your  duty  if  you  merely  accept  his  assurances 
that  everything  is  satisfactory.  The  tendency  to  ask,  '  What 
do  you  think  ?  '  and  then  chime  in  with  the  answer,  no 
matter  how  little  it  is  worth,  is  well  illustrated  by  the  story 
of  the  Frenchman  who  thought  he  would  play  a  trick  on  his 
fellow  townsmen,  and  went  up  the  street  telling  everybody 
he  met  that  there  was  a  whale  in  the  harbor;  but  when  the 
crowd  going  down  to  see  the  whale  became  very  large  he 
concluded  that  the  report  must  have  some  truth  in  it,  and 
went  himself. 

We  can  absorb  real  or  pretended  opinions,  but  we  cannot 


4°0  TESTIMONY. 

•weigh  evidence,  without  a  definite  problem.  Therefore 
whenever  we  assume  the  independent  position  of 
probiemand  a  judge  we  must  begin  by  finding  out  precisely 
deiiaiie.  what  it  is  that  we  have  to  decide.  This  is  often 
difficult;  for  we  cannot  make  our  questions 
definite  until  we  know  many  things  about  the  matter  with 
which  they  have  to  do.  We  must  therefore  keep  reframing 
the  vague  questions  with  which  we  started  and  making  them 
more  and  more  definite  as  our  knowledge  of  the  subject 
increases.  The  more  light  we  have  already  obtained  upon 
a  subject  the  more  we  can  break  our  questions  up,  and  the 
more  we  break  them  up  the  more  light  we  can  obtain. 
Hence  the  saying  that  it  is  as  hard  to  state  a  question 
properly  as  it  is  to  answer  it.  In  law  there  is  a  whole  system 
of  '  pleadings  '  which  must  be  conformed  to  in  every  civil 
suit  and  which  has  been  devised  for  the  express  purpose  of 
compelling  the  parties  to  come  at  last  to  some  one  definite 
'  issue  '  upon  which  the  whole  case  turns,  so  that  it  all  may 
be  settled  upon  the  strength  of  argument*  (if  it  be  a  ques- 
tion of  law)  or  of  testimony  (if  it  be  a  question  of  fact)  upon 
this  one  single  issue,  and  not  in  a  loose  way  upon  the  case 
as  a  whole,  f  In  history  or  in  science  we  cannot  always 

*  This  distinction  between  '  argument '  upon  a  '  question  of  law  '  and 
4  testimony  '  upon  a  'question  of  fact'  is  purely  technical.  The  true 
meaning  of  the  law,  as  intended  by  the  lawmakers  or  as  decided  in 
previous  cases,  is  as  much  a  question  of  fact  as  anything  else,  and  the 
'  argumer.t '  addressed  to  the  judge  is  a  presentation  and  explanation  of 
the  evidence  as  to  what  this  meaning  is,  precisely  as  the  examination  of 
•witnesses  and  the  address  to  the  jury  is  a  presentation  and  explanation 
of  the  evidence  concerning  other  facts. 

f  Civil  suits  and  criminal  proceedings  must  always  be  based  upon 
something  definite.  No  court  will  entertain  a  suit  for  general  injuries 
or  a  charge  of  general  misconduct.  When  the  plaintiff — to  take  a 
civil  suit — has  made  his  definite  '  declaration  '  he  must  serve  notice  of 
it  upon  the  defendant.  If  the  latter  makes  no  reply  within  a  specified 
period,  the  case  goes  against  him  by  default.  If  he  makes  one,  it  must 
be  as  definite  as  the  charge.  (I  a)  lie  may  '  demur  for  matter  of  form  ', 
or  say  that  the  charge  has  not  been  made  in  legal  form,  perhaps,  for  ex- 


MUST   HAVE  A   PROBLEM  AND  MAKE  IT   DEFINITE.   401 

reduce  everything  to  one  single  question,  for  our  interests 
are  manifold  and  one  aspect  of  a  case  may  be  quite  as  inter- 
esting as  another.  Yet  we  can  separate  our  questions  and 
discuss  them  one  at  a  time.  Often,  too,  we  can  find  some 
one  '  crucial  test ',  like  the  evidence  which  settles  the  vital 
issue  in  a  lawsuit,  by  which  each  one  of  them  can  be 
settled.  If  we  have  too  many  questions  in  mind  at  once, 
whether  they  be  relatively  independent  or  whether  several  of 
them  be  subsidiary  to  some  other,  we  are  almost  certain  to 
become  confused  or  to  neglect  some  aspects  of  the  case 
without  knowing  it,  and  thus  to  do  bad  work.  The  only 
safe  method  is  to  follow  the  example  of  the  courts  and  hear 
only  one  case  at  a  time,  reduce  this  case  to  as  simple  an. 
issue  as  possible,  and  dismiss  as  '  irrelevant '  every  alleged 
fact  that  does  not  bear  directly  upon  this  issue,  however 
interesting  the  fact  may  be  in  itself  and  however  important 
for  the  settlement  of  some  other  issue. 

The  lack  of  a  definite  problem  reduced  by  successive 
analyses  to  one  or  more  definite  issues,  and  the  lack  of  the 
consequent  sense  of  relevance  and  irrelevance,  is  particularly- 
ample,  that  it  is  too  indefinite.  (i  b)  He  may  '  demur  for  matter  of  sub- 
stance ',  or  say  that  there  is  no  reason  known  to  the  law  why  he  should 
not  do  the  very  thing  charged  against  him.  (2)  He  may  '  plead  by 
way  of  traverse ',  or  say  that  he  did  not  do  the  very  thing  charged. 
(3)  Finally,  he  may  '  plead  by  way  of  confession  and  avoidance  ',  or  say- 
that  he  did  do  it;  but  that  there  were  certain  other  facts,  which  he  speci- 
fies and  stands  ready  to  prove,  which  change  the  legal  aspect  of  the  case. 
By  compelling  the  defendant  to  make  some  one  of  these  answers  to  the 
charge  and  then  compelling  both  sides  to  stand  by  the  question  which  the 
pleadings  have  developed,  on  pain  of  losing  the  case,  the  court  succeeds 
in  reaching  an  issue  of  law  or  of  fact  about  which  the  two  sides  differ, 
and  which  is  definite  and  simple  enough  to  be  settled  reasonably.  If  the 
final  issue  be  one  of  law — raised  by  a  demurrer — it  is  settled  by  the 
judge  after  he  has  listened  to  argument.  If  it  be  one  of  fact,  it  is  settled 
by  the  jury  after  they  have  listened  to  the  evidence.  In  either  case  the 
argument  or  the  evidence  (as  it  may  be)  is  addressed  to  the  particular 
point  at  issue,  not  to  the  case  as  a  whole,  and  upon  it  the  whole  case 
depends. 


402  TESTIMONY. 

apparent  in  most  discussions  of  politics  and  history.  When 
it  comes  to  these  subjects  the  emotions  connected  with  our 
party  interests  and  party  traditions  make  analysis  especially 
difficult.  There  is  nothing  in  a  chemist's  emotions  to  keep 
him  from  regarding  a  pail  of  water  as  really  consisting  of  so 
many  separate  atoms  of  oxygen  and  hydrogen;  but  if  a  person 
has  been  brought  up  to  revere  the  Roman  Catholic  Church 
or  to  hate  the  Democratic  party,  there  is  much  in  his 
emotions  to  prevent  him  from  regarding  the  one  or  the  other 
as  nothing  but  a  number  of  separate  individuals  who  differ 
greatly  from  each  other  in  many  ways  and  are  determined  in 
their  acts  by  all  sorts  of  different  motives  and  external  influ- 
ences. What  is  true  of  groups  of  persons  is  true  also  of 
groups  of  events.  If  we  are  accustomed  to  feel  strongly 
about  some  great  historical  movement,  like  the  Reformation 
or  the  Civil  War,  our  emotions  make  it  difficult  for  us  to 
analyze  it  into  several  long  series  of  separate  acts,  and  to 
realize  that  while  each  individual  act  has  its  own  particular 
moral  relations  the  sum-total  can  hardly  be  said  to  have  any 
"whatever. 

Having  made  our  question  definite  we  must  not  attempt 
to  answer  it  from  the  impression  that  the  evidence  made 
Issue  before  before  we  did  so;  for  we  only  attend  to  the  parts 
evidence.  of  a  story  that  interest  us,  and  details  which  may 
be  of  the  highest  importance  for  the  settlement  of  some  par- 
ticular point  may  be  very  uninteresting  in  themselves,  and 
therefore  pass  unnoticed  when  they  are  told  before  the  point 
is  raised.  The  only  thing  to  do  is  to  go  over  every  bit  of 
the  evidence  again  with  each  new  question  and  pick  out  the 
parts  that  have  a  bearing  on  it.  Moreover,  we  should  do 
this  again  every  time  an  issue  is  split  up  into  others  more 
definite,  or  abandoned  for  others  more  appropriate.  A  story, 
for  example,  which  was  rejected  as  false  in  the  preliminary 
stages  of  an  inquiry  may  contain  some  phrase  or  some 
allusion  that  will  explain  the  whole  matter  when  the  problem 
is  reduced  to  its  last  analysis.  This  process  of  going  over 


MUST   NOT  BE  MANAGED   BY    THE   WITNESSES.     40 3 

all  the  evidence  afresh  with  each  new  question  is  not  so 
tedious  as  one  might  suppose,  for  the  new  question  always 
makes  us  see  the  evidence  in  a  new  light. 

The  strength  of  our  natural  tendency  to  decide  a  case  by 
our  first  impressions  and  to  neglect  the  later  evidence  is  well 
recognized  by  those  persons  who  take  care  to  have  their  own 
version  of  some  quarrel  told  first.  Here  again  the  law 
recognizes  our  weakness,  and  not  only  provides  that  the 
judge  and  jury  shall  always  hear  both  sides  of  a  case,  but  also 
determines  the  order  in  which  they  shall  be  heard,  and  pro- 
vides that  after  the  evidence  has  all  been  given  each  side 
shall  have  an  opportunity  to  review  it  and  point  out  its 
bearing?. 

When  we  are  determining  the  precise  nature  of  our 
problem  and  sifting  the  evidence  by  which  it  is  to  be  settled, 
the  witnesses  with  whom  we  have  to  deal  will  Must  not  be 
often  try  to  mislead  us.  They  will  appeal  to  theDwft-by 
our  emotions.  They  will  try  to  make  us  sub-  nesses- 
stitute  some  other  issue  for  the  real  one.  They  will  intro- 
duce all  kinds  of  irrelevant  matter  to  distract  our  attention, 
and  when  they  do  they  will  make  it  as  interesting  as  they 
possibly  can.  At  the  same  time  they  will  pass  as  lightly  and 
indifferently  as  possible  over  the  points  which  are  of  real 
value  for  the  decision  of  the  case.  If  they  are  compelled  to 
dwell  upon  them,  they  may  try  hard  to  make  what  they  have 
to  say  so  tedious  that  we  will  not  listen  to  it,  or  so  obscure 
that  we  shall  stop  trying  to  understand  it.  But  in  spite  of 
all  these  artifices  we  must  never  let  a  witness  determine  what 
issue  or  what  part  of  the  evidence  we  shall  attend  to.  TQ 
be  sure  we  cannot  put  him  on  the  rack  to  make  him  tell 
the  truth;  but  we  must  always  remember  that  it  is  we  and 
not  he  who  is  judging,  and  therefore  we  must  not  say  '  Yes  ' 
when  we  do  not  understand ;  we  must  not  be  afraid  to  cross- 
examine  him  on  the  points  that  we  think  essential  (instead 
of  those  on  which  he  invites  us  to  examine  him) ;  and  we 
must  not  stop  the  examination  when  the  witness  seems  to 


404  TESTIMONY. 

think  it  has  gone  far  enough,  for  fear  that  if  we  do  not  he 
will  think  us  hostile  or  distrustful  or  stupid. 

Finally,  if  we  really  mean  to  settle  our  questions  rationally, 
we  must  never  settle  them  while  we  are  confused  or  excited 

or  while  there  is  reason  to  believe  that  we  have 
decide  in  a  not  yet  found  or  sifted  all  the  evidence  worth 

considering.  The  impulse  to  have  done  with 
deliberation  and  get  things  settled  one  way  or  the  other  is 
very  strong,  and  like  every  other  impulse  it  has  its  value; 
but  when  we  set  out  to  decide  a  question  on  rational  grounds 
it  is  out  of  place  and  we  must  resist  it.  Strangely  enough, 
when  we  are  trying  to  discover  new  truths  the  very  presence 
of  this  impulse  is  the  best  possible  sign  that  we  should  act 
against  it,  for  it  only  arises  when  all  the  evidence  will  not  fit 
together  easily  according  to  our  preconceived  notions,  and 
that  is  the  only  circumstance  under  which  there  can  be  any- 
thing essentially  new  to  discover.  We  must  resist  also  the 
tendency  to  be  hurried  by  the  impatience  of  others.  We 
cannot  yield  to  it  without  sacrificing  the  independence  which 
it  was  necessary  to  assume  when  we  set  out  to  judge  for 
ourselves  instead  of  blindly  following  the  leader  or  the  crowd. 
Indeed  the  attempts  which  others  make  to  hurry  us  are 
sometimes  only  a  device  to  keep  us  from  finding  the  truth. 
If  in  any  particular  case  there  is  not  enough  evidence  to 
settle  a  question  rationally,  we  should  leave  it  unsettled — not 
settle  it  irrationally.  A  good  way  to  guard  ourselves  against 
the  tendency  to  jump  to  conclusions  when  the  evidence  is 
only  half  weighed  is  always  to  ask  whether  the  evidence  on 
which  we  act  would  satisfy  some  cooler  critic  to  whom  we 
might  submit  it.  The  best  judges  are  those  whose  decisions 
are  reversed  least  often  by  the  higher  courts. 


CHAPTER    XXXVI. 
THE    THREE   ULTIMATE    TESTS   OF   TRUTH. 

MUCH  has  been  said  in  the  foregoing  chapters  about  ways 
of  testing  truth.  Something  must  be  said  now  about  the 
ultimate  tests  to  which  all  others  can  be  reduced.  Of  these 
there  are  three  :  Consistency,  Conceivability,  and  Uniformity 
including  Simplicity.  We  apply  the  test  of  consistency  be- 
cause we  are  rational  beings  who  recognize  that  two  incom- 
patible states  of  affairs  cannot  both  exist ;  we  apply  the  test 
of  conceivability  because  we  have  the  gift  of  imagination  as 
well  as  reason,  and  we  believe  that  if  certain  relations  are  not 
imaginable,  they  cannot  exist  ;  and  we  apply  the  test  of  uni- 
formity and  simplicity  because  as  active  beings  it  is  easier  for 
us  to  do  something  old  and  simple  than  something  new  and 
complex.  These  three  tests  may  not  be  equally  decisive,  but 
each  has  its  own  sphere,  and  in  that  sphere  it  is  the  best  that" 
we  can  get. 

The  test  of  Consistency  was  considered  at  length   in  the 
discussion  of  deduction.      We  saw  that  statements  may  be 
regarded  as  inconsistent  not  merely  when  they 
directly  contradict  each  other,  but  also  whenever 
one  of  them  asserts  the  existence  of  a  state  of  affairs  that  is 
incompatible  for  any  reason  whatever  with  the  state  of  affairs 
asserted  by   the  other.     We  saw,  too,  that  in  order  to  tell 
whether  one  supposed  state  of  affairs  really  is  incompatible 
with  another  we  must  know  something  about  how  the  world 
is  actually  constituted.    This  appeal  to  the  actual  constitution 

405 


406         THE   THREE   ULTIMATE   TESTS   OF   TRUTH. 

of  things  vastly  increases  the  number  of  cases  to  which  the 
test  of  consistency  can  be  applied  ;  but  it  cannot  help  weak- 
ening it,  for  there  is  always  a  question  of  whether  things 
really  are  constituted  as  we  suppose,  and  before  this  question 
can  be  answered  we  are  often  thrown  back  upon  one  or  both 
of  the  other  tests,  and  that,  too,  perhaps  by  some  process 
that  is  vague,  indirect,  or  complicated. 

The  test  of  Conceivability,  or  rather  of  Inconceivability, 
for  it  is  the  negative  relation  that  is  decisive,  is  illustrated 
Conceiv-  best  'in  geometry.  We  believe  that  two  straight 
ability.  lines  cannot  enclose  a  space,  because  we  cannot 
possibly  imagine  or  picture  two  lines  which  look  straight — 
i.e. ,  look  as  though  they  ran  evenly  in  one  direction  through- 
out their  whole  course — and  at  the  same  time  look  as  though 
they  enclosed  a  space.  We  believe  that  the  circumference 
of  a  circle  is  curved  in  one  place  precisely  as  in  another  be- 
cause we  cannot  possibly  picture  a  figure  that  looks  as  though 
it  conformed  with  the  ordinary  definition  of  a  circle — i.e., 
looks  as  though  every  part  of  the  circumference  were  exactly 
the  same  distance  from  some  one  point  within  it— and  at  the 
same  time  looks  as  though  the  curvature  of  the  circumference 
were  not  the  same  throughout ;  and  because  the  more  unequal 
the  curvature  of  a  circumference  appears  to  be  the  more  un- 
equal also  appear  to  be  the  radii. 

What  is  true  of  the  definitions,  axioms,  and  postulates  of 
geometry  is  true  also  of  the  demonstrations.  They  too  appeal 
to  the  fact  that  we  cannot  picture  it  otherwise.  Suppose  it  is 
a  question  of  proving  that  the  three  angles  of  a  plane  triangle 
are  together  equal  to  two  right  angles.  The  student  goes 
through  the  demonstration  with  reference  to  the  figure  given 
in  the  book,  and  then  if  he  is  not  convinced  he  tries  to  draw 
some  kind  of  triangle  to  which  the  demonstration  will  not 
apply,  and  he  feels  sure  of  the  demonstration  only  when  he 
has  convinced  himself  that  no  matter  how  hard  he  tries  he 
can  never  imagine  a  plane  triangle  so  drawn.  Thus  the  first 
principles  and  the  demonstrations  of  geometry  both  depend 


CONCEIVABIL1TY.  407 

upon  certain  limitations  of  our  imagination.  We  believe 
them  to  be  true  because  we  cannot  picture  the  contrary. 

There  are  two  objections  that  may  be  raised  against  geom- 
etry as  a  demonstrative  science.  The  first  is  that  there  may 
not  be  such  a  thing  in  the  whole  world  as  an  absolutely 
straight  line,  an  absolutely  round  circle,  an  absolutely  per- 
fect triangle,  and  so  on.  How  can  we  say,  the  objector  asks, 
that  things  must  be  so  when  in  reality  they  may  never  be  so  ? 
The  second  objection  is  this:  Even  if  our  geometrical  con- 
ceptions do  agree  with  things  as  they  happen  to  exist  in  this 
world,  how  can  we  say  that  anything  must  agree  with  these 
conceptions  when  for  all  we  know  there  may  be  some  other 
world  in  which  they  do  not  agree  at  all — some  world  in  which 
straight  lines  can  enclose  spaces  and  in  which  plane  triangles 
do  not  have  their  three  angles  together  equal  to  two  right 
angles  ? 

The  answer  to  the  first  of  these  objections  is  that  geometry 
is  not  primarily  concerned  with  the  question  of  whether 
things  have  certain  forms  or  not,  but  only  with  the  mutual 
relations  of  those  forms  themselves  as  we  have  to  conceive 
of  them.  It  does  not  say  that-such  things  as  perfectly 
straight  lines  exist  in  the  real  world,  but  only  that  if  they 
do,  no  one  or  two  of  them  can  enclose  a  space  ;  and  to 
find  out  what  a  straight  line  is  we  go  to  our  own  imagina- 
tions, and  not  to  the  world  of  reality.  It  is  true  that 
geometry  uses  real  diagrams,  but  the  force  of  a  demon- 
stration does  not  lie  merely  in  the  fact  that  we  cannot  put  a 
certain  combination  of  relations  on  a  blackboard  or  a  piece  of 
paper  without  also  putting  in  a  second  or  leaving  out  a  third; 
but  rather  in  the  further  fact  that  we  cannot  imagine  what 
the  impossible  combination  would  be  like  if  we  could  put  it 
there.  It  is  not  the  physical  impossibility,  but  the  incon- 
ceivability, that  appeals  to  us.  If  it  were  a  mere  question  of 
physical  fact,  the  force  of  every  demonstration  would  depend 
upon  the  accuracy  with  which  the  figures  are  ruled  and  meas- 
ured; but  it  does  not.  Whether  perfectly  straight  lines  and 


408         THE   THREE   ULTIMATE   TESTS   OF   TRUTH. 

perfectly  round  circles  are  ever  found  in  the  world  is  a  ques- 
to  be  settled  outside  of  geometry  and  wholly  irrelevant  to  it. 

As  to  the  other  objection — that  in  some  other  world  the 
fundamental  relations  of  figures  in  space  might  all  be  turned 
topsy-turvy — the  answer  is  that  if  it  were  so  and  if  we  were 
moved  there,  unless  we  also  were  changed  we  could  never 
see  it.  We  should  undoubtedly  find  that  things  did  not 
come  out  as  we  expected,  and  it  might  be  that  we  could 
stumble  across  some  algebraic  formulae  (like  those  applicable 
to  the  "  fourth  dimension  ")  by  which  we  could  learn  to 
adjust  ourselves  to  their  vagaries;  but  unless  we  ourselves 
were  transformed  or  enlarged  along  with  our  world  we 
should  be  no  more  able  to  see  and  imagine  the  new  relations 
than  a  musician  can  hear  and  feel  perfect  harmony  and 
melody  in  the  chaotic  strumming  of  a  child.  If  we  picture 
things  at  all,  we  have  to  picture  them  as  we  can.  When  we 
talk  about  lines  and  size  and  shape  and  direction  our  words 
have  no  meaning  unless  they  refer  to  something  which  is  at 
least  partly  picturable;  and  if  we  cannot  even  begin  to  pic- 
ture a  kind  of  shape  or  direction  that  meets  a  given  descrip- 
tion, we  have  a  right  to  conclude  that  it  is  not  picturable 
and  therefore  is  not  really  a  shape  or  direction  at  all.  And 
this  is  just  as  true  whether  the  shape  and  direction  spoken 
of  are  supposed  to  be  only  imaginary  or  to  be  real.  So  that 
the  test  of  conceivability  which  is  applicable  in  the  first  in- 
stance to  mere  images  as  images  can  be  applied  also  to  the 
relations  of  things  which  are  assumed  to  be  imaginable. 

The  danger  attending  the  test  of  conceivability  is  that 
we  may  apply  it  where  we  should  not.  Geometry  deals  only 
with  the  arrangement  of  points  and  lines  in  space,  and  if 
some  relation  has  nothing  to  do  with  space,  we  must  not 
deny  its  existence  because  we  cannot  make  a  drawing  of  it. 
Nobody  denies  the  existence  of  a  song  because  the  tones 
cannot  be  arranged  in  triangles  and  circles,  or  of  a  feeling 
of  remorse  because  we  cannot  picture  it  as  lying  to  the  right 
or  to  the  left  of  the  knowledge  that  goes  along  with  it.  In 


THE   THIRD   TEST.  409 

the  same  way  no  one  has  any  right  to  deny  the  existence  of 
a  soul  merely  because  \ve  cannot  represent  it  as  round  or 
square,  yellow  or  green,  loud  or  soft,  or  literally  sweet  or 
sour. 

Our  third  ultimate  test  of  truth  depends  upon  our  animal 
organization  as  creatures  who  form  habits  and   Th  tj.ird 
tend  in  other  ways  also  to  do  whatever  must  be   test- 
done  for  our  preservation  and  welfare,  in  the  shortest  and 
easiest  way  possible. 

We  have  seen  how  the  tendency  to  make  uniform  reactions 
leads  to  the  judgment  that  what  we  react  upon  is  uniform, 
and  how  this  uniformity  that  we  find  because  we  look  for  it 
is  thought  of  as  involving  a  vast  number  of  permanent 
Things,  each  of  which  belongs  to  some  definite  Kind,  and 
acts  in  the  same  Way  as  every  other  member  of  the  Kind 
under  the  same  Conditions.  We  have  seen,  too,  how  some 
apparent  anomaly  is  '  explained  '  when  it  is  shown  that  in 
spite  of  appearances  it  is  still  a  case  of  these  same  uni- 
formities; and  how  an  interpretation  of  any  particular  ex- 
perience which  cannot  show  how  that  experience  grows  out 
of  these  uniformities  is  branded  as  false  and  unhesitatingly 
abandoned  for  one  which  can. 

But  the  test  of  truth  growing  out  of  our  organization  as 
active  creatures  does  not  end  here;  for  it  may  be 
that   each   of  two   or  more  explanations  of  an  SfthTSass. 
experience  is  consistent  with  these  uniformities, 
and  still  we  are  able  to  choose  between  them,  even  though 
it  be  without  quite  so  much  certainty. 

It  will  be  remembered  that  we  came  to  seek  for  uniformity 
in  the  ultimate  elements  of  which  things  and  situations  are 
composed  because  we  were  often  disappointed  in  our  efforts 
to  find  it  in  the  complex  things  and  situations  as  a  whole. 
But  it  was  in  the  complex  mass  that  we  looked  for  it  at  first. 
The  first  things  that  we  notice  and  learn  to  separate  from 
the  confused  mass  around  us  are  not  definite  details  which 
we  afterwards  build  up  into  more  complex  wholes,  but  more 


410         THE   THREE   ULTIMATE   TESTS  OF  TRUTH. 

or  less  vague  wholes  which  we  afterwards  analyze  into  the 
more  definite  details:  we  can  recognize  a  person  as  a  whole 
before  we  can  describe  a  single  feature.  And  so  the  first 
uniformities  we  expect  are  not  uniformities  in  the  definite 
details  that  we  have  not  noticed,  but  in  the  vague  wholes 
that  we  have.  When  two  wholes  present  about  the  same 
general  appearance  they  call  from  us  the  same  rather  vague 
and  clumsy  act,  and  we  never  think  of  fine  distinctions 
between  either  the  wholes  to  which  we  react  or  the  reactions 
themselves  until  we  find  that  a  reaction  which  gives  us  what 
we  want  in  one  case  will  not  do  so  in  another.  Then  per- 
force, wre  are  driven  to  notice  some  detail  in  which  the  two 
cases  differed;  and  by  a  repetition  of  this  process  we  reach 
at  last  the  ultimate  things  and  relations  to  which  we  feel 
that  the  law  of  uniformity  applies  without  exception. 

But  in  spite  of  the  disappointments  which  teach  us  that  it 
is  only  in  the  ultimate  details  that  we  can  be  absolutely 
certain  of  our  uniformities,  we  still  continue  to  look  for  them 
with  considerable  confidence  in  the  mass  also.  '  Appear- 
ances ',  or  general  impressions,  would  not  be  '  deceitful '  if 
they  never  deceived;  and  they  could  not  deceive  if  we  had 
no  tendency  to  trust  them.  We  should  not  hear  people  say, 
'  It  is  strange  how  much  difference  a  little  thing  often 
makes,'  if  they  were  not  in  the  habit  of  ignoring  the  little 
things  and  looking  at  the  larger  wholes. 

Thus  we  never  lose  the  tendency  to  look  for  uniformity  in 
the  general  appearance  of  things  as  well  as  in  their  ultimate 
relations,  and  thus  it  happens  that  when  there  are  two  possi- 
ble explanations  for  some  state  of  affairs  which  are  equally 
satisfactory  in  the  various  details,  we  naturally  choose  the 
one  which  gives  the  greater  impression  of  uniformity  in  the 
mass.  The  '  catastrophic  '  theory  of  the  earth's  history, 
which  supposed  the  structure  of  its  crust  to  have  been  pro- 
duced by  a  series  of  changes  more  violent  than  those  with 
which  we  are  familiar,  might  have  given  a  perfectly  satis- 
factory account  of  all  the  details  under  consideration,  and  yet 


UNIFORMITY   IN   THE  MASS.  411 

it  would  still  have  been  abandoned  as  soon  as  Lyell  showed 
that  these  details  could  all  be  accounted  for  just  as  well — 
I  do  not  say  better,  for  that  is  not  my  point — by  processes 
of  the  sort  that  are  going  on  around  us  all  the  time. 

This  tendency  to  prefer  accounts  of  things  which  make 
what  is  distant  in  time  and  space  as  similar  as  possible  to 
what  we  perceive  about  us  is  due  in  part  to  the  law  of 
association.  The  feeling  of  belief  is  subject  to  this  law  like 
any  other  thought  or  feeling;  and  the  more  a  new  concep- 
tion is  like  one  we  are  accustomed  to  believe  in,  the  more  it 
tends  to  arouse  the  same  feeling  of  belief  by  its  very  likeness. 
In  the  same  way,  if  a  new  conception  bears  a  strong  total 
likeness  to  one  which  we  are  accustomed  to  reject,  we  tend 
through  the  law  of  association  to  reject  it.  We  act  towards 
ideas  precisely  as  we  act  towards  people,  liking  those  that 
look  like  our  old  friends,  and  disliking  those  that  bear  a 
strong  resemblance  to  our  old  enemies. 

Another  reason  why  it  is  easier  1o  believe  in  things  like 
those  to  which  we  are  accustomed  than  in  those  that  are 
not  is  that  it  is  easier  to  conceive  of  them.  If  we  have  no 
ear  for  music,  we  cannot  realize  what  it  is,  and  so  we  can 
hardly  help  thinking  that  the  enjoyment  which  others  profess 
to  get  out  of  it  is  largely  affected;  if  we  have  never  been  on 
the  edge  of  nervous  prostration,  we  are  likely  to  believe  that 
the  utter  exhaustion  which  others  sometimes  say  they  feel  is 
merely  '  imagination  '  or  an  empty  excuse  for  laziness;  if  we 
have  never  suffered  great  pain,  we  are  inclined  to  think  that 
it  cannot  be  so  very  terrible;  and  if  we  have  never  done  a 
generous  deed  or  sacrificed  ourselves  for  a  principle,  we  are 
likely  to  find  nothing  in  stories  of  such  devotion  but  veiled 
selfishness  and  hypocrisy.  We  cannot  realize  what  these 
things  mean,  and  so  we  do  not  believe  in  them. 

What  is  true  of  these  simple  feelings  and  motives  is  true 
also  of  things  and  situations  that  are  more  complex.  We 
sometimes  read  in  books  on  psychology  that  if  we  have  a 
separate  knowledge  of  each  of  the  elements  that  enter  into 


412         THE   THREE   ULTIMATE   TESTS   OF   TRUTH. 

some  situation,  we  can  put  them  all  together  and  thus 
imagine  the  situation  as  a  whole.  But  this  is  no  easy 
matter.  We  may  know  the  meaning  of  every  word  in  a 
description,  but  unless  the  thing  described  bears  some  total 
resemblance  to  something  with  which  we  are  familiar  it  is 
extremely  difficult  to  conceive  of  the  separate  details  at  once 
and  hold  them  together  in  such  a  way  as  to  get  anything 
like  a  reliable  conception  of  the  whole.  Experience  begins 
with  wholes  and  not  with  parts;  and  it  is  a  great  deal  easier 
to  construct  a  new  whole  by  modifying  an  old  one  something 
like  it  than  by  laboriously  fitting  and  holding  together  a 
large  number  of  details.  Indeed  this  is  the  way  we  almost 
always  proceed.  And  from  this  it  follows  that  the  more 
total  resemblance  a  new  thing  is  supposed  to  bear  to  some- 
thing with  which  we  are  familiar  the  easier  it  is  to  conceive 
of  it,  and  the  less  total  resemblance  it  is  supposed  to  bear 
to  anything  with  which  we  are  familiar  the  harder  it  is  to 
conceive  of  it.*  And  when  it  comes  to  a  question  of  what 
we  shall  believe,  the  relatively  familiar  conception  is  likely 

*  This  of  course  is  the  psychological  law  of  apperception,  and  it  ex- 
plains the  old  rule  that  definition  should  be  by  genus  and  difference 
rather  than  by  an  enumeration  of  all  the  generic  qualities  as  well  as  the 
specific  in  detail. 

Complexity  and  novelty  produce  a  certain  inconceivability,  but  it  is 
relative,  and  must  be  distinguished  very  sharply  from  the  absolute  incon- 
ceivability that  was  discussed  a  few  pages  back.  Even  when  relations 
are  so  very  complex  that  we  feel  sure  no  human  mind  could  possibly 
picture  them  all  together  (e.g.,  the  position  of  every  atom  in  an  ink- 
bottle),  nobody  believes  that  this  kind  of  inconceivability  proves  the 
relations  to  be  impossible.  Because  we  cannot  think  of  a  great  many 
things  at  the  same  time  we  never  think  of  denying  that  they  can  exist 
together.  We  recognize  that  the  discrepancy  is  due  to  our  own  weak- 
ness ;  to  a  certain  fluidity  of  mind  which  makes  it  impossible  to  hold 
more  than  a  few  relations  steadily  before  us  at  once.  The  kind  of  in- 
conceivability that  we  discussed  before  seems,  on  the  other  hand,  to  be 
due  rather  to  a  certain  mental  firmness  or  rigidity  :  the  relations  keep 
their  place  quite  steadily;  and  somehow  we  cannot  make  them  bend  to 
fit  each  other. 


ANALOGY.  413 

to  be  present  and  available  when  the  less  familiar  has  become 
too  vague  and  shadowy  to  be  taken  hold  of. 

Thus  the  more  some  new  state  of  affairs  resembles  one  to 
which  we  are  accustomed  the  easier  it  is  to  believe  in  it,  if 
for  no  other  reason,  merely  because  it  is  easier  to  conceive 
of  it. 

When  two  things  or  situations  resemble  each  other  closely 
as  a  whole  as  well  as  in  many  of  their  details,  there  is  a  fair 
presumption  that  they  resemble  each  other  also 
in  some  other  detail.  The  close  resemblance 
between  Mars  and  the  earth  in  many  known  respects  makes 
it  more  or  less  probable  that  Mars  resembles  the  earth  also 
in  being  inhabited;  and  the  close  resemblance  between  the 
lower  animals  and  man  in  a  multitude  of  other  respects 
makes  it  probable  that  those  animals  resemble  man  also  in 
possessing  consciousness.  Arguments  of  this  sort  are  said 
to  be  '  from  Analogy  '.  Such  arguments  are  never  absolutely 
conclusive. 

In  general,  the  larger  the  proportion  of  respects  in  which 
the  things  compared  are  known  to  resemble  each  other  and 
the  stronger  the  resemblance  in  each,  the  stronger  is  the 
argument.  But  where  the  matter  in  question  is  known  to 
be  specially  connected  with  some  known  point  of  resem- 
blance or  difference,  general  resemblance  or  difference  does 
not  count  for  so  much.  However  much  the  moon  may  be 
like  the  earth  in  other  respects,  the  one  fact  that  it  has  no 
atmosphere  is  proof  positive  that  it  has  no  inhabitants  like 
ourselves. 

Many  so-called  arguments  from  analogy  are  little  more 
than  metaphors,  and  quite  worthless  as  arguments:  e.g.,  the 
argument  that  a  mother  country  has  a  right  to  regulate  the 
internal  affairs  of  a  colony  because  a  mother  has  a  right  to 
absolute  control  over  her  young  daughter;  or  the  argument 
that  parliamentary  government  is  always  bound  to  fail 
because  'victories  may  be  won  by  a  poor  general,  but  nevel 
by  a  debating  society  '. 


414        THE  THREE  ULTIMATE  TESTS  OF  TRUTH. 

Any  decidedly  new  idea  may  be  rejected  as  '  absurd  ' ;  but 
when  it  is  not  merely  new  but  also  contrary  to  our  accus- 
tomed modes  of  thought  the  rejection  is  more 
Absurdity. 

emphatic  and  the  term  seems  more  appropriate. 

To  believe  in  something  that  is  merely  different  from  what 
we  have  been  accustomed  to  requires  that  we  shall  form 
a  new  habit  of  thought;  to  believe  in  something  directly 
opposed  to  what  we  are  accustomed  to  requires  that  we 
shall  break  up  an  old  one,  and  for  people  old  enough  to 
have  fixed  habits  this  is  often  much  more  difficult.  We  are 
inclined  to  object  to  it  in  precisely  the  same  way  as  we 
might  object  to  having  our  things  put  away  in  some  new 
place,  or  wearing  skirts  instead  of  trousers,  or  living  under  a 
new  kind  of  government,  or  leaving  old  friends  and  associat- 
ing with  old  enemies.  The  new  arrangement  seems  intrinsi- 
cally bad,  but  in  reality  the  badness  lies  only  in  its  relation 
to  us.  It  is  bad  merely  because  it  is  new,  and  a  person 
accustomed  to  it  would  find  ours  just  as  bad.  So  it  is  with 
beliefs.  Apart  from  contradictions  there  is  no  such  thing 
as  an  idea  which  is  absurd  in  itself,  and  when  we  reject  a 
new  view  as  absurd  it  is  not  because  our  reason  sees  the 
absurdity;  on  the  contrary,  it  seems  absurd  because  our 
habits  compel  us  to  reject  it.  Thus  we  use  Absurdity  as  a 
test  of  truth,  not  because  we  have  concluded  beforehand 
that  the  test  is  reasonable,  but  merely  because  we  are 
creatures  of  habit  and  cannot  help  it. 

Often  the  absurdity  of  a  new  view  appears  not  so  much  in 
the  bare  outline  as  in  the  details.  We  try  to  think  them  all 
out  according  to  the  new  idea,  but  we  keep  putting  in  the 
old  ones  until  at  last  we  get  a  hopeless  confusion  of  the  new 
and  the  old,  and  then  we  say,  See  how  inconsistent  and 
ridiculous  this  new  view  is!  Thus  when  Columbus  suggested 
that  there  might  be  land  on  the  other  side  of  the  world  as  a 
kind  of  counterpoise  to  Europe,  his  critics  replied  that  that 
was  impossible;  for  if  there  were  land  there,  the  inhabitants 
•would  have  to  walk  upon  their  heads  (since  their  feet  would 


ABSURDITY.  415 

be  up,  towards  the  sky  above  Europe,  and  their  heads  would 
be  down).  This  filling  out  of  the  details  according  to  old 
habits  is  often  almost  as  true  of  those  who  embrace  the  new 
idea  as  of  those  who  reject  it.  The  new  doctrine  may  fill 
them  with  a  grand  enthusiasm ;  but  when  it  comes  to  work- 
ing out  the  details  the  old  ideas  keep  coming  back  to  give 
the  new  words  their  meaning:  '  New  Presbyter  is  but  old 
Priest  writ  large  ',  and  a  revolution  of  any  sort  retains  vastly 
more  of  the  past  than  those  who  are  in  it  realize.* 

Because  the  impression  of  Absurdity  (as  distinguished 
from  contradiction  and  true  inconceivability)  depends  upon 
a  breach  with  established  ways  of  thinking  rather  than  upon 
any  intrinsic  imperfection  in  the  idea  itself,  there  is  hardly 
an  idea  which  has  not  seemed  absurd  to  somebody  at  some 
time.  The  King  of  Siam  in  the  traveller's  story  refused  to 
believe  the  absurd  tale  that  water  sometimes  got  solid;  to 
Aristotle  it  was  absurd  to  suppose  that  slavery  should  cease 
to  exist,  or  looms  work  without  hands;  and  so  with  others 
it  seemed  absurd  to  suppose  that  the  tradition  of  the  elders 
might  be  superseded;  that  a  good  thing  could  come  out  of 
Nazareth;  that  a  man  should  love  his  enemy;  that  a  law- 
observing  Pharisee  might  be  no  better  at  heart  than  a  law- 
breaking  publican;  that  the  earth  moves;  that  a  man  might 
rightly  disobey  the  king;  that  there  are  no  ghosts  or 
witches;  that  slavery  is  not  a  divine  institution;  that  men 
and  monkeys  had  the  same  ancestors;  that  steam  could  be 
made  to  do  work;  that  it  is  possible  to  travel  sixty  or  eighty 
miles  an  hour,  talk  with  people  hundreds  of  miles  away,  see 
through  solid  boards,  or  read  at  your  breakfast-table  in 
America  what  they  did  in  Europe  on  the  same  day  at  noon. 

These  examples  show  how  unreliable  the  test  of  absurdity 
is  ;  and  yet,  in  spite  of  its  unreliability,  we  should  be  abso- 
lutely helpless  without  it :  the  victims  of  every  passing  sug- 

*  This  explains,  too,  the  many  '  rebukes '  that  Jesus  had  to  give  his 
disciples.  Again  and  again  the  old  ways  of  thinking  would  return  and 

they  had  to  be  told,  "  Ye  know  not  what  manner  of  spirit  ye  are  of." 

> 


416         THE   THREE   ULTIMATE   TESTS   OF   TRUTH. 

gestion,  utterly  devoid  of  all  stability  of  thought  or  purpose 
and  absolutely  incapable  of  anything  like  steady  progress. 

Just  as  novelty  gives  the  impression  of  absurdity,  so  famili- 
arity removes  it.  Repeat  a  suggestion  or  a  statement  often 
enough  and  the  sense  of  incongruity  gradually  wears  away 
and  the  mind  at  last  becomes  '  open  '  to  it.  In  this  way  mere 
habituation — the  mere  continued  effort  to  see  things  from 
the  new  standpoint — often  does  more  to  produce  conviction 
than  argument.  With  such  a  thing,  for  example,  as  James's 
doctrine  that  the  bodily  '  expression  '  of  an  emotion  deter- 
mines the  feeling,  and  not  vice  versa,  students  may  think  they 
see  how  much  force  there  is  in  the  argument  at  once,  but 
they  really  do  not  feel  its  force  until  after  they  get  used  to 
the  conception.  When  they  have  learned  to  find  their  way 
around  in  it  they  may  accept  it  genuinely,  but  not  before. 

Sometimes  it  is  possible  to  remove  the  sense  of  absurdity 
from  a  conception  almost  instantly  by  showing  that  though  it 
seems  strange  it  is  really  very  much  like  some  other  to  which 
we  are  accustomed.  That  the  Roentgen  rays  should  pene- 
trate solid  boards  seems  very  marvellous,  and  had  the  facts 
been  less  well  authenticated  those  who  heard  the  story  when 
it  was  new  might  well  have  said  it  was  much  too  absurd  to 
be  true  ;  but  when  we  are  reminded  that  common  light-waves 
pass  through  glass  as  thick  and  solid  as  the  boards,  it  is  easier 
to  believe  the  story  of  the  Roentgen  rays. 

When  two  explanations  are  equally  good  in  other  respects 

we  tend  to  choose  the  simpler,  and  we  feel   that 
Simplicity.  r    .  ' 

somehow  or  other  the  choice  is  justifiable. 

We  tend  to  believe  in  a  simple  state  of  affairs  rather  than 
a  complex,  just  as  we  tend  to  believe  in  a  familiar  rather  than 
an  unfamiliar — for  one  thing — merely  because  the  former  is 
clearly  remembered  when  the  occasion  for  explanation  arises, 
while  the  latter  is  confused  or  forgotten.  This  is  one  reason. 
But  then,  again,  even  when  two  explanations  are  conceived 
with  equal  clearness  and  equally  well  remembered  we  cannot 
help  regarding  the  simpler  one  as  '  better'.  All  explanation 


SIMPLICITY.  417 

is  an  attempt  to  find  uniformity  behind  apparent  disorder  or 
anomalies,  and  the  simpler  the  total  state  of  affairs  which  we 
suppose  to  be  there  the  more  apparent  and  striking  is  the 
uniformity.  A  simple  explanation  is  always  more  '  beauti- 
ful '  than  a  complex.  Then,  again,  in  the  third  place,  we 
ourselves,  as  creatures  of  limited  time  and  strength,  are 
always  accustomed  to  accomplish  our  own  ends  by  the  sim- 
plest means  possible  and  to  see  others  do  the  same.  Sim- 
plicity of  means  thus  becomes  a  very  practical  ideal  which 
we  seek  both  to  realize  and  to  find  in  all  human  affairs  ;  and 
when  we  come  to  deal  with  Nature  the  force  of  habit  carries 
us  on  to  seek  for  it  there  also,  as  though  we  knew  beforehand 
that  Nature  were  the  product  of  some  intelligent  being  work- 
ing for  ends  like  ours  according  to  our  ideals.  Leibnitz 
says  :  "True  physics  must  be  derived  really  from  the  source 
of  the  divine  perfections.  It  is  God  who  is  the  final  reason 
of  things,  and  the  knowledge  of  God  is  no  less  the  principle 
of  the  sciences  than  his  essence  and  his  will  are  the  principles 
of  beings.  The  most  reasonable  philosophers  agree  to  this, 
but  there  are  very  few  of  them  who  can  make  use  of  it  to 
discover  truths  of  importance.  .  .  .  Far  from  excluding  final 
causes  and  the  consideration  of  a  being  acting  with  wisdom, 
it  is  from  thence  that  all  must  be  derived  in  physics."  * 

I  do  not  think  that  one  needs  to  know  about  God  or  to 
believe  in  him  in  order  to  seek  for  ends  and  simplicity  and 
other  forms  of  rationality  in  Nature  ;  but  rather,  on  the  con- 
trary, that  it  is  because  we  cannot  help  seeking  for  these  that 
we  do  believe  in  him. 

The  rule  of  simplicity  in  explanation  was  laid  down  as  a 
formal  principle  by  the  Franciscan  monk  William  of  Occam, 
in  these  words  :  Enlia  non  sunt  muliiplicanda  pnetcr  necessi- 
tatem.\  This  is  known  as  Occam's  Razor,  or  the  Law  of 

*  Letter  to  Bayle,  1687.    Duncan's  '•  Philosophical  Works  of  Leibnitz  ", 

PP-  35.  36- 

f  '  We  must  not  assume  the  existence  of  any  more  things  than  neces- 
sary.' Occam  died  in  1347.  Petrus  Areolus.  another  Franciscan,  who 


41 8        THE  THREE  ULTIMATE  TESTS  OF  TRUTH. 

Parsimony.  He  used  the  razor  to  good  effect  to  get  rid  of 
the  abstractions  which  the  recognized  philosophy  of  his  time 
took  for  things.*  But  nowadays,  when  explanations  are 
concerned  quite  as  much  with  the  laws  of  action  as  with  the 
things  that  are  supposed  to  act,  we  may  interpret  the  princi- 
ple to  mean  not  merely  that  the  things  we  assume  to  exist  or 
to  be  present  must  not  be  more  numerous  than  necessary, 
but  also  that  the  laws  must  not  be  more  complex.  The 
things  we  assumed  would  be  unnecessarily  numerous  if  we 
supposed  that  God  created  the  world  through  the  efforts  of 
a  dozen  different  grades  of  inferior  spirits,  when  all  the  facts 
would  be  explained  just  as  well  on  the  assumption  that  he 
did  it  all  himself.  The  laws  we  assumed  would  be  unneces- 
sarily complex  if  we  supposed  that  the  planets  moved  in 
cycles  and  epicycles  instead  of  in  simple  ellipses,  or  that 
elements  did  not  combine  chemically  in  simple  proportions, 
but  according  to  some  very  complex  law  that  led  to  the  same 
practical  results. 

When  we  try  to  make  every  explanation  as  simple  as  pos- 
sible we  are  confronted  by  several  dangers.  The  first  of  these 
is  that  we  shall  find  simplicity  by  ignoring  some  essential  part 
of  the  facts  we  are  trying  to  explain.  The  theory  that  every 
voluntary  act  is  done  for  the  sake  of  gaining  pleasure  or  avoid- 
ing pain  is  extremely  simple  and  it  can  be  made  to  explain  a 
great  many  facts  of  conduct;  but  it  certainly  ignores  the  things 
that  people  sometimes  do,  knowing  all  the  time  that  they 
will  lead  in  the  end  to  far  more  pain  than  pleasure.  The 
theory  that  fear  is  due  to  a  perception  of  danger  will  explain 
a  great  deal ;  but  it  cannot  explain  why  children  often  sud- 
denly and  spontaneously  begin  to  be  afraid  of  things  that 
have  never  hurt  them,  or  why  many  adults  show  inordinate 

died  in  1321,  had  said  the  same  thing  in  these  words  :  Non  est  philoso- 
phicum,  pluralitatem  rerum  ponere  sine  causa ;  frustra  enim  fit  per 
plura  quod  fieri  potest  per  pandora. 

*  "  Sujficiunt  singularia,  et  it  a  tales  res  universalia  omnino  frustra 
ponuntur." 


SIMPLICITY.  419 

fear  of  such  things  as  <:ats,  mice,  caterpillars,  and  common 
snakes,  which  they  know  perfectly  well  to  be  harmless. 
Thus  the  alleged  explanation  is  too  simple;  for  it  ignores  an 
important  part  of  the  facts  to  be  explained. 

The  second  danger  is  that  of  attaining  simplicity  in  explana- 
tion by  ignoring  the  relations  of  the  facts  we  are  trying  to 
explain  to  the  rest  of  the  world.  The  ideal  of  all  science  and 
philosophy  is  the  simplest  possible  connected  view  of  the 
whole  universe;  but  in  trying  to  attain  it  we  must  not  be 
penny  wise  and  pound  foolish.  There  is  a  difference,  as 
Kipling  says,  between  a  team  of  good  players  and  a  good 
team  of  players ;  and  there  is  a  difference  between  a  set  of 
good  explanations  and  a  good  set  of  explanations.  A  simple 
explanation  of  some  one  little  fact  that  will  not  fit  in  with 
our  explanations  of  the  rest  of  the  world  is  not  so  satisfactory 
as  a  more  complicated  explanation  that  will.  Suppose,  for 
example,  that  the  old  witchcraft  and  demonology  or  that  the 
modern  telepathy  and  spiritualism  gave  or  could  be  made  to 
give  a  perfectly  simple,  coherent,  and  well-articulated  expla- 
nation of  the  particular  set  of  facts  with  which  they  deal.  The 
explanation  given  would  be  extremely  unsatisfactory,  and 
would  doubtless  be  rejected  by  many  scientists  as  wholly  unsci- 
entific, so  long  as  there  was  no  way  of  fitting  the  telepathic  and 
spiritualistic  conception  of  things  in  with  the  vast  and  ever- 
growing mass  of  facts  that  are  being  continually  explained 
and  coordinated  more  and  more  closely  every  day  from  other 
points  of  view.  If  the  facts  that  the  telepathists  and  spirit- 
ualists deal  with  can  be  explained  piecemeal  by  principles 
recognized  elsewhere,  no  scientist  doubts  that  such  an  ex- 
planation is  far  better  than  one  by  thought-transference  and 
spirits,  although  the  latter  might  be  a  great  deal  simpler  so 
far  as  the  one  set  of  facts  was  concerned. 

It  was  some  such  feeling  as  this  of  opposition  to  the  intro- 
duction of  totally  new  principles  of  explanation  serviceable  in 
only  one  special  field  that  Newton  expressed  in  his  celebrated 
dictum  :  Hypotheses  non  Jingo.  The  cause  which  we  assign 


420         THE   THREE  ULTIMATE   TESTS   OF   TRUTH. 

for  any  known  effect  must  be,  he  said,  vera  causa:  a  true 
cause,  or  one  for  whose  existence  we  have  more  evidence  than 
can  be  found  in  the  special  facts  that  it  is  invoked  to  explain. 
A  third  danger  connected  with  the  principle  of  simplicity 
is  the  opposite  of  that  just  explained.  It  is  undoubtedly 
true  that  a  complicated  explanation  of  the  facts  in  some  one 
field,  that  fits  in  with  what  we  know  about  all  the  rest  of  the 
world,  is  better  than  a  simple  explanation  that  does  not,  and 
it  is  just  as  true  that  we  must  not  accept  the  new  set  of  causes 
until  we  have  made  a  reasonable  effort  to  explain  the  various 
facts  in  question  by  old  ones;  and  yet,  on  the  other  hand,  we 
must  not  carry  our  rejection  of  strange  causes  to  an  extreme. 
If  the  alleged  new  principle  does  nothing  else,  it  may  serve  to 
hold  together  a  mass  of  facts  many  of  which  would  otherwise 
escape  us  or  become  hopelessly  confused,  and  to  keep  us 
puzzled  until  we  find  some  other  explanation  that  is  better. 
In  this  way  even  a  false  hypothesis  is  often  better  than  none 
at  all.  And  then,  again,  it  may  turn  out  that  our  discon- 
nected principle  is  not  false  after  all.  It  is  true  that  our  sci- 
entific ideal  is  a  simple,  well-coordinated  view  of  the  world 
as  a  whole;  but  it  is  also  true  that  we  are  a  long  way  from 
attaining  it.  What  we  possess  in  the  way  of  knowledge  is 
not  so  much  one  field  that  is  always  growing  broader  as  a 
large  number  of  fields  each  of  which  is  growing  out  towards 
the  others  so  that  sometimes  they  meet ;  but  there  are  still 
plenty  of  gaps,  and  we  must  not  always  refuse  to  cultivate 
some  new  field  because  we  do  not  see  how  it  can  be  joined 
with  the  rest.  It  is  nearly  as  bad  to  try  to  make  our  differ- 
ent hypotheses  consistent  with  each  other  too  soon  as  not  to 
try  to  do  so  at  all.  The  Greek  philosophers  except  Aristotle 
were  always  thinking  about  the  sum-total  of  things,  and 
Aristotle  is  the  only  one  of  them  who  made  anything  like  a 
respectable  contribution  to  science.  Descartes  was  thinking 
about  the  ultimate  relations  of  mind  and  matter,  and  his  gen- 
eral standpoint  compelled  him  to  say  that  the  lower  animals 
were  mere  automata  :  mechanical  toys  that  cried  when  you 


THE   RIGHT   TO   ASSUME   THESE   PRINCIPLES.      421 

kicked  them,  just  as  a  bell  rings  when  you  shake  it,  without 
any  feeling  whatever. 

Thus  the  Principle  of  Simplicity  or  Parsimony  is  one  that 
we  are  compelled  to  follow,  but  often  it  is  hard  to  tell  whether 
we  will  not  reach  it  sooner  in  the  end  by  leaving  it  for  the 
moment. 

Of  course  it  is  one  thing  to  be  so  organized  that  the  sim- 
ple and  familiar  are  more  easily  believed  in  than  the  compli- 
cated and  unfamiliar,  and  a  somewhat  different 
thing  to  accept  the  formal  principle  that  where  assume  these 
there  are  t\vo  theories,  equally  good  in  other  re- 
spects, that  which  assumes  the  simpler  and  more  familiar  state 
of  affairs  is  the  more  likely  to  be  true.  And  yet  if  we  have 
the  organization,  we  can  hardly  avoid  the  principle.  To  say 
that  the  simpler  and  more  familiar  is  more  easily  believed 
in  means  that  in  most  cases  we  do  believe  in  it,  or,  in 
other  words,  that  in  most  cases  the  relatively  simple  and 
familiar  state  of  affairs  is  what  we  call  the  '  true  '  one  ;  and 
now,  a  large  number  of  particular  cases  being  settled,  all  we 
have  to  do  is  to  compare  them  and  we  reach  our  formal  prin- 
ciple :  The  theory  which  supposes  the  simpler  and  more 
familiar  state  of  affairs  is  more  often  true  than  the  other.* 

It  is  because  we  act  on  this  principle  of  discrediting  the 
new,  whether  we  ever  state  it  in  words  or  not,  that  the  phrase 
'  a  very  strange  story  '  generally  means  a  lie. 

So  much  for  the  fact  that  we  actually  do  use  Consistency, 
Conceivability,  and  Uniformity  and  Simplicity  as  tests  of 
truth,  and  even  for  the  further  fact  that  we  come  to  think  we 
have  a  right  to.  But  have  we  this  right?  Is  it  possible  to 
prove  that  there  is  such  a  relation  in  the  world  as  com- 

*  We  get  the  principle  when  we  reflect  enough  to  see  the  results  of 
our  own  organization  (i.e.,  to  see  that  all  our  explanations  are  rela- 
tively simple)  but  not  enough  to  see  that  they  arc  the  results  of  that 
organization  (i.e.,  that  these  explanations  are  simple  because  the  sim- 
ple ones  are  those  we  chose).  When  we  see  that  the  question  takes  a 
new  form. 


422         THE   THREE   ULTIMATE   TESTS   OF   TRUTH. 

patibility  or  incompatibility?  Can  we  prove  that  anything 
real  conforms  or  ought  to  conform  to  the  laws  of  our  imagi- 
nation ?  Hardest  of  all,  can  we  prove  that  because  some- 
thing is  uniform  or  simple  and  therefore  easy  for  us  to  think 
of,  it  is  any  easier  on  that  account  for  it  to  exist?  And  if 
\ve  cannot  prove  these  things,  have  we  any  real  right  to  use 
the  tests?  My  answer  so  far  as  uniformity  is  concerned  has 
been  given  already  in  Chapter  XXII.  I  believe  that  we 
cannot  prove  these  things,  and  therefore  cannot  prove  our 
right  to  use  the  tests.  We  simply  take  them  for  granted  and 
take  the  right  to  use  the  tests  for  granted  along  with  them. 

The  time  has  gone  by  long  since  when  wise  men  sought 
for  a  philosophy  without  assumptions;  and  if  we  cannot  get 
along  without  them  in  philosophy,  we  certainly  cannot  get 
along  without  them  in  common  life  and  in  the  logic  that  tries 
to  serve  as  a  guide  for  common  life.  If  any  one  believes,  as 
Kant  did,  that  not  only  colors  and  sounds  and  smells  and 
tastes,  but  also  Space  and  Time  with  all  their  relations  of 
shape,  size,  distance,  direction,  duration,  coexistence,  and 
succession,  are  purely  human  ways  of  imagining  things  and 
do  not  really  belong  to  things  in  themselves  at  all,  then  that 
person  ought  not  to  use  conceivability  as  a  test  of  what  things 
in  themselves  can  or  cannot  be.  If  any  one  has  meditated 
about  these  topics  so  long  that  it  no  longer  seems  to  him 
absurd  to  doubt  the  simplicity  and  general  rationality  of 
Nature,  I  do  not  see  how  it  is  possible  to  restore  his  faith  by 
demonstration  ;  and  if  he  has  emancipated  himself  from  the 
bonds  of  habit  so  completely  that  he  really  doubts  the  ex- 
istence of  those  principles  of  uniformity  that  we  indicate  by 
the  words  Thing  and  Kind  and  Cause  and  Law,  then  there  is 
certainly  no  way  of  proving  to  him  that  one  explanation  is 
better  than  another,  or  indeed  that  anything  needs  explana- 
tion at  all.  If,  finally,  he  really  and  truly  doubts — as  Des- 
cartes tried  to — the  existence  of  everything  but  his  own  pass- 
ing thought,  I  do  not  see  how  we  could  prove  to  his  satis- 
faction that  there  is  a  real  nature  of  things  in  virtue  of 


THE  LIMITS   OF   PROOF.  423 

which  one  supposed  fact  is  incompatible  with  another,  and 
therefore  that  there  really  is  such  a  thing  as  a  contradiction. 

If  people  actually  doubt  all  these  things,  we  do  not  argue 
with  them  :  we  lock  them  up  instead,  and  by  this  resort  to 
brute  force  we  confess  defeat  in  the  field  of  pure  argument. 
If,  on  the  other  hand,  they  profess  to  doubt  them,  but  show  by 
their  acts  or  their  argument — perhaps  by  the  very  fact  of  talk- 
ing with  us — that  when  they  are  off  their  guard  they  really  take 
them  for  granted,  the  most  we  can  do  is  to  point  out  the  incon- 
sistency, with  the  hope  that  their  faith  in  law  and  a  nature 
of  things  is  so  strong  at  bottom  that  inconsistency  in  an 
argument  will  seem  to  them  a  fault.  We  cannot  go  beyond 
this  appeal  to  faith.  Thus  we  start  with  faith  in  experience 
as  a  whole,  however  vaguely  we  may  conceive  of  this  experi- 
ence ;  but  such  a  faith  implies  also  faith  in  all  the  ultimate 
principles  that  that  experience  involves. 

There  are  some  questions  which  logic  and  its  tests  of  truth 
will  never  help  us  to  settle.  If  it  is  a  question  whether  a 
certain  state  of  affairs  exists,  and  if  there  is  no 
objection  so  far  as  consistency  and  conceivability  ^proof!*8 
are  concerned  to  believing  that  it  does,  the  only 
way  of  settling  the  question  is  to  ask  whether  any  one  lias 
observed  the  state  of  affairs  itself  or  anything  that  can  be 
recognized  as  its  necessary  cause  or  effect.  If  we  cannot 
observe  the  state  of  affairs  itself  and  if  we  cannot  prove  that 
anything  which  we  do  observe  must  be  connected  causally 
with  something  of  the  sort,  we  cannot  prove  that  it  exists. 
But  if  the  state  of  affairs  in  question  is  one  that  might  exist 
without  being  observed  or  producing  unmistakable  effects,  we 
cannot  prove  either  that  it  does  not  exist.  It  may  be  that 
there  are  mountains  on  the  other  side  of  the  moon  ;  but  we 
cannot  see  them,  and  we  do  not  know  of  any  change  that 
they  would  make  in  what  we  do  see  if  they  were  there  ;  con- 
sequently we  cannot  tell  whether  they  are  there  or  not.  It 
may  be  that  plants  feel,  that  they  enjoy  the  sunlight  and 
the  rain  and  suffer  discomfort  in  the  cold;  but  feelings  can 


424         THE   THREE   ULTIMATE   TESTS   OF   TRUTH. 

never  be  perceived  directly  except  in  ourselves,  and  we  have 
no  idea  what  change  their  presence  or  their  absence  would 
make  in  the  behavior  of  a  plant,  and  so  we  can  never  know 
whether  plants  have  them  or  not.  It  may  be  that  every 
living  soul  existed  on  the  earth  before  in  the  body  of  some  man 
or  beast  although  it  has  forgotten  what  took  place  in  its  life 
there;  but  no  one  knows  how  the  life  of  a  reincarnated  soul 
should  differ  from  that  of  one  that  never  lived  before,  and  so 
no  one  can  ever  tell  from  what  he  observes  whether  the  theory 
of  transmigration  is  true  or  not.  It  may  be,  finally,  that  the 
world  was  created  in  infinite  love  and  wisdom  and  that  all 
our  human  experiences  are  intended  as  preparations  for  some 
glorified  life  after  death  ;  but  no  one  knows  enough  about 
infinite  love  and  wisdom  to  say  how  a  world  made  by  it 
would  differ  from  any  other  world,  or  how  a  life  intended  by 
the  Creator  as  a  preparation  for  another  would  differ  from 
one  which  was  not ;  and  therefore  nothing  that  we  observe 
in  the  world  can  prove  the  matter  one  way  or  the  other. 

What  we  believe  about  questions  like  these  is  not  inferred 
by  logical  processes  from  what  we  observe  in  the  world;  but 
is  added  to  what  we  observe,  as  a  matter  of  religious  faith. 
Such  a  faith  gives  our  experiences  a  new  kind  of  significance  ; 
but  no  particular  experience  of  the  sort  that  science  deals 
with  can  either  confirm  or  refute  that  faith  ;  and  this  is  why 
different  people  often  give  diametrically  opposite  religioi.s 
interpretations  to  the  same  concrete  experiences. 

It  often  seems  indeed  to  persons  of  a  certain  temperament 
or  character  that  some  observable  fact  is  a  sufficient  proof  cf 
what  they  believe  about  religion  ;  and  perhaps  they  make 
long  abstract  arguments  to  show  it  ;  but  abstract  arguments 
are  hard  to  criticise  in  any  case,  and  it  requires  an  unusual 
amount  of  intellectual  honesty  and  energy  to  seek  for  obscure 
fallacies  in  arguments  that  profess  to  prove  what  we  already 
believe  or  wish  to  believe  ;  and  so  this  appearance  of  logical 
proof  is  easy  enough  to  account  for. 

There  is   only  one  way  in  which  logic  or  a   knowledge  of 


THE   LIMITS   OF   PROOF.  425 

scientific  method  can  help  us  in  matters  of  this  kind.  It  can 
show  us  its  own  limitations,  and  save  us  in  this  way,  on  the 
one  hand,  from  the  trouble  of  constructing  long  and  labored 
arguments  that  do  not  prove  anything,  and,  on  the  other,  from 
the  error  of  supposing  that  the  absence  of  proof  in  favor  of 
certain  beliefs  can  be  taken  as  any  argument  against  them. 

Science  and  faith,  particularly  religious  faith,  are  often 
supposed  to  be  in  some  kind  of  logical  conflict  with  each 
other.  But  this  is  a  mistake.  Science  itself  rests  on  faith, 
for  it  assumes,  as  we  have  seen,  that  there  is  such  a  thing  as 
a  world  beyond  one's  own  individual  sensations,  and  that 
that  world  really  possesses  the  uniformity  and  coherence 
which  we  feel  impelled,  as  creatures  of  habit,  to  read  into  it. 
Indeed  what  we  call  scientific  '  knowledge '  is  simply  an  in- 
terpretation that  we  give  to  our  experience  or  some  of  it  on 
the  basis  of  this  faith.  But  a  faith  in  uniformity  and  coher- 
ence is  certainly  not  inconsistent  with  a  faith  in  purpose  and 
wisdom  and  goodness  also,  and  the  mere  fact  that  science 
does  not  attempt  to  unify  experience  from  the  standpoint  of 
this  latter  faith  as  well  as  from  that  of  the  former  is  no  rea- 
son why  the  scientist  should  not  do  so  when  he  leaves  his 
science  and  begins  to  think  of  something  else.  Religion 
cannot  tell  what  the  world  looks  like,  and  science  cannot  tell 
anything  about  its  spiritual  values ;  but  for  this  very  reason 
the  one  is  no  more  inconsistent  with  the  other  than  geom- 
etry or  psychology  is  inconsistent  with  aesthetics  or  juris- 
prudence. 


NOTE. 

SOME  of  the  following  examples  for  which  no  credit  is 
given  are  used  in  many  different  books,  and  I  have  not  taken 
the  trouble  to  trace  their  origin.  The  initials  after  others 
should  be  interpreted  as  follows: 

C,  for  J.  E.  Creighton's  "  Introductory  Logic"; 

D,  for  N.  K.  Davis's  "  Theory  of  Thought  "; 

F,  for  Thomas  Fowler's  "  Elements  of  Deductive  Logic  "  ; 
H,  for  J.  H.  Hyslop's  "  Elements  of  Logic  "; 
J,  for  W.  S.  Jcvons's  "  Elementary  Lessons  in  Logic  ",  or 
his  "  Studies  in  Deductive  Logic  "  ; 

W,  for  Archbishop  Whately's  "  Elements  of  Logic  ". 

426 


EXERCISES. 

WITH  every  chapter  students  are  advised  to  make  use  of  the 
marginal  summaries  or  the  table  of  contents  to  assist  them  in 
review,  thus:  What  are  the  two  kinds  of  thinking?  What  is 
the  nature  of  judgments  and  propositions,  and  how  are  they 
related  to  eacii  other? 


CHAPTER   I. 

i.  Estimate  the  value  of  the  following  arguments: 

(a)  Tolstoi's  interpretation  of  Christianity  must  be  false;  for 
if  it  is  correct  we  and  our  ancestors  have  not  been  Christians 
at  all. 

(fi)  You  may  have  an  ape  for  an  ancestor  if  you  want  to ;  but 
I  don't  care  for  one. 

(r)  "  To  believe  that  man  was  aboriginally  civilized  and  then 
suffered  utter  degradation  in  so  many  regions,  is  to  take  a  pitia- 
bly low  view  of  human  nature.  It  is  apparently  a  truer  and 
more  cheerful  view  that  progress  has  been  much  more  general 
than  retrogression;  that  man  has  risen,  though  by  slow  and 
interrupted  steps,  from  a  lowly  condition  to  the  highest  stand- 
ard as  yet  attained  by  him  in  knowledge,  morals,  and  religion." 
(Darwin's  "Descent  of  Man  ",  end  of  Chap.  V.) 

(<i )  Of  course  you  ought  to  be  good,  for  you  belong  to  a 
church  and  go  to  prayer-meeting;  but  I  make  no  professions. 

(/.')  If  he  thinks  it  is  wrong,  it  is  wrong  for  him  ;  but  with  me 
the  case  is  very  different,  for  I  never  thought  it  was  wrong. 

(/)  It  is  all  very  well  for  you  to  talk;  but  if  these  ideals  of 
yours  are  so  very  beautiful,  why  don't  you  put  them  into 
pract  ice  ? 

(g}  '  Is  there  a  hell?' — That  depends  altogether  upon  your 
point  of  view. 

427 


428  EXERCISES. 

(h)  "  But  if  there  be  no  resurrection  from  the  dead,  then  is 
Christ  not  risen;  and  if  Christ  be  not  risen,  then  is  our  preach- 
ing vain  and  your  faith  is  also  vain."  (I.  Cor.  xv.  13,  14.) 

(*')  You  say  that  '  of '  is  a  preposition,  but  that  cannot  be  ;  for 
in  the  very  sentence  in  which  you  say  so  it  is  a  noun. 

(j)  '  W£  know  what  we  mean  by  clear  water  or  a  clear  atmos- 
phere, then  why  shouldn't  we  know  what  we  mean  by  clear 
ideas?'  'I  suppose  you  mean  that  a  hazy  atmosphere  is  one 
that  you  can  see  and  that  a  clear  atmosphere  is  one  that  you 
can  not  see,  and  that  in  the  same  way  the  clearest  ideas  are  the 
only  ones  that  we  can  not  see.' 

(/£)  Charlemagne  is  king;  king  is  four  letters;  therefore 
Charlemagne  is  four  letters. 

(/)  I  cannot  accept  your  opinion  as  true,  for  it  seems  to  me 
that  its  general  recognition  would  be  attended  with  the  most 
injurious  consequences  to  society.  (F.) 

2.  What  is  the  best  way  to  persuade  the  slothful  man  that 
there  is  no  lion  in  the  way  ? 

3.  Is  there  any  objection  to  the  following? — "General  names 
are  predicable  of  individuals  because  they  possess  certain  attri- 
butes ;   to  predicate  the  possession  of  those  attributes  is  the 
same  thing  as  to  predicate  the  general  name." 


CHAPTER    II. 

1.  What  is  the  meaning  of  the  word  '  doubt  '  in  the  following 
lines  ? — 

Doubt  that  the  stars  are  fire  ; 

Doubt  that  the  sun  doth  move  ; 
Doubt  truth  to  be  a  liar  ; 

But  never  doubt  I  love. 

2.  Explain  the  following : 

The  good  are  envied  of  the  bad,  and  glory  finds  disdain, 
And  people  arc  in  constancy  as  April  is  in  rain. 

3.  What  is  the  meaning   of  the  word  'or'  in  the  following 
sentences? — 'John    or  James   will  do';    'Sodium    chloride   or 
common  salt  is  always  present ' ;  '  Clergymen  or  lawyers  always 
get  in  '. 


EXERCISES.  429 

4.  What  is  meant  by  the  following  statements,  and  in  what 
sense  is  the  second  of  them  true  ? — 

(a)  Our  team  wins  every  year,  except  in  off  years. 

(b)  No  one's  burden  is  ever  greater  than  he  can  bear. 

5<*.  What  is  meant  by  'the  people  '  in  the  phrase  "Govern- 
ment of  the  people,  for  the  people,  by  the  people  "  ? 

5^.  What  was  meant  by  the  statement  that  ail  men  are  born 
free  and  equal?  In  what  sense  of  the  words  is  it  true  ? 

5^.  In  the  exercises  to  Chapter  V  are  two  passages  from 
Bacon.  Find  the  meaning  of  all  the  words  used  there  in  an 
obsolete  or  peculiar  sense. 

6.  Define  the  terms  '  Wealth  ',  '  Capital ',  '  Society  ',  '  Friend  ', 
'  Courage  ',  '  House  ',  '  Savage  ',  '  Nice  ',  '  Lady  ',  '  Pious ',  '  Poor 
man  ',  '  The  weak  ',  '  Educated  ',  '  Circle  ',  '  Triangle  ',  '  Sopho- 
more'.  Why  are  the  last  three  words  more  easily  defined  than 
the  others  ? 

/.   Criticise  the  following  arguments  : 

(a)  The  college  chapel  is  sacred ;  for  a  chapel  is  a  kind  of 
church,  and  the  Church  is  a  divine  institution. 

(b}  This  stove  saves  half  the  ordinary  amount  of  fuel ;  there- 
fore two  such  stoves  would  save  it  all. 

(c}  A.  B.  is  professor  of  religion  in  the  university,  but  as  he 
is  very  irreligious  he  does  not  possess  the  religion  he  professes ; 
he  is  therefore  a  hypocrite. 

(d~)  All  presuming  men  are  contemptible;  this  man  therefore 
is  contemptible,  for  he  presumes  to  believe  his  opinions  are 
correct.  (J.) 

(e)  It  is  good  to  be  great  and  it  is  right  to  be  good  ;  Napoleon 
was  great ;  therefore  it  is  right  to  be  like  Napoleon. 

(f)  A  thoughtless  person  does  not  think;  one  who  does  not 
think  cannot  form  a  judgment;  therefore  a  thoughtless  person 
cannot  form  a  judgment. 

(£•)  It  is  wrong  to  criticise  an  inspired  book;  the  historians 
apply  criticism  to  the  Bible  ;  therefore  they  do  wrong. 

(//)  No  evil  should  be  allowed  that  good  may  come  of  it ;  all 
punishment  is  an  evil;  therefore  no  punishment  should  be 
allowed  that  good  may  come  of  it. 

(7)  Whatever  is  dictated  by  Nature  is  allowable;  devoted- 
ness  to  the  pursuit  of  pleasure  in  youth,  and  to  that  of  gain 
in  old  age,  are  dictated  by  Nature ;  therefore  they  are  allow- 
able. (W.) 


43°  EXERCISES. 

8.  A  hunter  is  trying  to  shoot  a  squirrel  that  is  clinging  tc  a 
stump,  and  goes  all  around  the  stump  to  find  him  ;  but  the 
squirrel  always  keeps  on  the  opposite  side  of  the  stump.     Does 
the  hunter  go  around  the  squirrel? 

9.  Which  hen  is  the  mother  of  the  chicken,  the  one  that  laid 
the  egg,  or  the  one  that  hatched  it  out  and  takes  care  of  it  ? 

10.  What  is  the  true  significance  of  the  last  two  questions  ? 

11.  Analyze  the  following  explanations,  arguments,  and  defi- 
nitions : 

(a)  These  two  elements  almost  always  unite  when  they  are 
put  together,  for  they  have  an  affinity  for  each  other. 

(b)  It  is  harder  to  slide  on  wood  than  on  ice,  because  the  fric- 
tion is  greater. 

(c)  Movement  catches  the  attention,   and    therefore  we   are 
more  likely  to  notice  a  moving  object  than  one  that  remains 
stationary. 

O/)  It  is  always  wrong  to  lie  ;  for  any  departure,  for  any 
reason  whatever,  from  the  one  invariable  law  of  absolute 
veracity  is  always  reprehensible. 

(e)  An  archbishop  is  one  who  discharges  archiepiscopal 
functions. 

(_/)  Habit  can  be  defined  as  '  the  purgatory  in  which  we 
atone  for  our  past  misdeeds  '. 

(£•)  "  A  definition  is  the  exposition  of  the  connotation  of  a 
term." 

(/i)  Definition  is  the  enumeration  of  the  parts  of  an  idea. 

(/)  The  process  by  which  the  qualities  that  belong  to  an 
object  is  defined  is  called  logical  definition. 

(/)  "  Despite  the  hot  weather  two  cases  of  smallpox  were 
discovered  yesterday.  .  .  .  The  discovery  of  these  occasional 
cases,  the  health  authorities  say,  is  evidence  that  the  plague  is 
still  prevalent  in  the  city." 

12.  Make  five  arguments  that  turn  upon  ambiguous  words, 
five   purely  verbal  explanations,  and  five  purely  verbal  defini- 
tions. 

13.  Define  all  the    important  words   in    the   Declaration    of 
Independence  or  some  other  connected  discourse. 

14.  Is  any  fault  to  be  found  with  any  of  the  following  rules 
for  definition  or  the  way  in  which  they  are  stated  ? — 

(a)  A  definition  should  contain  the  essential  attributes  of  the 
word  or  object  being  defined. 


EXERCISES  431 

(b)  A  definition    should  contain  an  adequate  description  of 
the  term  defined. 

(c)  The  subject  of  a  definition  must  be  exactly  equivalent  to 
the  predicate. 

(<•/)  A  definition  must  not  be  defined  by  figurative  or  ambigu- 
ous terms:  Death  is  an  undisturbed  sleep  (figurative). 

(e)  The  definition  must  be  equivalent  to  the  term  defined: 
Rhubarb  is  a  plant  (which  can  be  eaten). 

( f )  A  definition  must  state  the  essential  qualities  of  the  term 
defined :     A    classical    student   is   one  who    has   studied    Latin 
(Greek  is  also  essential). 

(g}  Give  all  the  essential  qualities  of  the  species  to  which  the 
object  defined  belongs. 

15.  Criticise  the  following  definitions  : 

(<n)  A  JUDGMENT  is  a  conclusion  reached  after  considering 
certain  previous  propositions  upon  the  same  subject  but  pre- 
senting different  views. 

(a2)  Judgment  is  the  conclusion  arrived  at  after  correct, 
logical  analysis  of  a  matter. 

(113)  Judgment  is  estimating  the  relative  value  of  things. 

(<*4)  Judgment  is  the  comparison  of  two  or  more  simple 
apprehensions. 

(ii$)  A  judgment  is  an  inference  made  from  material  gained 
by  reasoning. 

(a6)  Judgment  is  logical  conclusion  drawn  from  given  hypo- 
thesis. 

(ay)  Judgment  is  the  process  of  clear  thinking,  of  estimating 
accurately,  and  finally  of  reaching  a  decision. 

(aS)  A  judgment  is  the  expression  of  a  belief,  conclusion, 
determination,  and  the  like. 

(ay)  Judgment  is  a  statement  which  affirms  or  denies  some- 
thing. 

(aio)  Judgment  is  that  act  of  the  mind  by  which  we  deduce 
from  two  statements  a  third. 

(an)  Judgment  is  anything  which  when  stated  will  form  a 
proposition. 

(1112)  Judgment  is  a  decision  as  to  the  truth  or  falsity  of  a 
statement. 

(61)  A  PROPOSITION  is  a  phrase  that  expresses  a  thought  in 
form  of  a  subject  and  predicate  ;  a  judgment,  the  predicate 
giving  some  relation,  condition,  or  quality  of  the  subject. 


43  -  EXERCISES. 

(b2)  A  proposition  is  a  thought  expressed  in  the  form  of  a 
sentence,  consisting  of  subject  and  modifiers,  predicate  and 
modifiers,  and  copula. 

(£3)  A  proposition  is  a  statement  which  contains  a  subject 
and  predicate  and  forms  a  part  of  a  syllogism. 

(l>4)  A  proposition  is  an  equation  consisting  of  a  subject 
term,  a  predicate  term,  and  a  copula. 

(^5)  A  proposition  is  a  statement  of  a  true  or  false  fact. 

(b6)  A  proposition  is  an  assertion  which  expresses  a  declara- 
tion either  positive  or  negative. 

(b~j}  A  proposition  is  a  statement  in  the  form  of  a  gram- 
matical sentence  which  affirms  or  denies  a  fact. 

(<£8)  A  proposition  is  a  statement  that  asserts  something. 

(kg)  A  proposition  is  a  statement  which  must  contain  a  sub- 
ject and  predicate;  in  which  the  predicate  asserts  or  denies  or 
questions  a  relation  existing  between  it  and  the  subject. 

(c\)  SUBJECT  of  a  proposition  is  that  of  which  something  is 
affirmed. 

(c2)  The  subject  of  a  proposition  is  the  word  about  which 
something  is  said  ;  eg.,  The  book  is  lying  on  the  table. 

(^3)  The  subject  of  a  proposition  is  the  object  or  objects 
about  which  a  statement  is  made. 

(<r4)  The  subject  of  a  proposition  is  that  of  which  something 
is  affirmed  or  denied  by  the  verb  and  rest  of  the  proposition. 

(cy)  The  subject  of  a  proposition  is  the  object  of  discourse. 

(c6)  The  subject  of  a  proposition  is  the  name  of  an  object  or 
substance  concerning  which  a  statement  is  made  in  the  predi- 
cate term. 

(c.'7)  The  subject  of  a  proposition  is  a  word  or  group  of  words 
about  which  something  is  said. 

(6-8)  The  subject  of  a  proposition  is  that  about  which  some 
statement  is  made.  It  includes  the  word  and  all  of  its  modi- 
fiers. 

(^•9)  The  subject  of  a  proposition  is  a  word,  phrase,  or  clause 
— -  which  something  is  affirmed  or  denied  in  the  predicate. 


EXERCISES.  433 


CHAPTER    III. 

1.  Summarize  the  opening  lines  of  "Paradise  Lost"  in  the 
plainest  and  most  concrete  language  possible,  getting  rid  of  all 
the  figures  of  speech  and  abstract  terms,  but  giving  their  mean- 
ing in  the  simplest  prose.     Make  summaries  also  of  as    many 
paragraphs  as  possible  from  Berkeley's  "  Principles  of  Human 
Knowledge",  of  the  editorials  in  the  morning  paper,  and  of  a 
couple  of  pages  from  some  such  book  as  Mrs.  Eddy's  "  Science 
and  Health  ".     In  making  these  summaries  be  careful  to  put  in 
all  the  little  connecting  words,  such  as  'and  ',  'or',  'because', 
4  therefore',  '  in  other  words  ',  etc. ;  use  your  own  language,  not 
that  of  the  author  summarized  ;   and  take  care  to  make  your 
meaning  absolutely  clear  and  unambiguous,  even  if  you  have  to 
give  several  alternative  interpretations  to  a  passage. 

Why  is  it  that  some  of  these  summaries  are  harder  to  make 
than  others?  Is  it  because  the  subject-matter  is  more  difficult 
or  because  the  writer's  ideas  are  more  hazy  ? 

2.  Explain   the  meaning   of  the  law   of  gravitation  ;   of  the 
formulae  on  pp.  170,  175,  263,  265,  278,  and  292  of  this  book; 
and  of  any  other  formulae  that  seem  rather  hard  and  complex. 

3.  Determine  exactly  what  was  meant   by  each  one  of  the 
Ten  Commandments,  and    show  where   we    might   commit   a 
fallacy  of  Accident  or  Accent  in  interpreting  them. 

4.  What  fallacy  did  Bismarck  commit  in  his  abridgment  of 
the  Ems  despatch  ?   and    what    fallacy  did  Columbus  commit 
when  he  proved  that  an  egg  could  stand  on  end  ?     (J.) 

5.  In  what  sense  is  it  true  and  in  what  sense  is  it  false  that 
"  There  is  nothing  either  good  or  bad,  but  thinking  makes  it 
so  "  ? 

6.  What  fallacy,  if  any,  is  to  be  found  in  the  following  argu- 
ments : 

(<?)  You  say  now  that  you  never  believed  in  the  war  with 
Spain,  and  yet  you  voted  for  it  ;  for  you  voted  for  the  Repub- 
lican ticket  when  their  platform  had  already  declared  in  favor 
of  intervention,  and  everybody  knew  that  intervention  meant 
war. 

(b)  It  is  right  to  help  the  needy ;  therefore  it  is  right  to  give 
to  this  beggar,  for  he  is  needy. 


434  EXERCISES. 

(c)  In    going  around  the  world  westward  we  keep  gaining 
time,  and  the  whole  trip  would  gain  us  a  full  day  ;  therefore  if 
we  could  make  the  complete  journey  in  twenty-four  hours  it 
would  really  take  us  no  time  at  all. 

(d)  It  is  not  true  that  on  the  first  of  next  month  John  Smith 
will  become  the  husband  of  Miss  Brown;  he  will  become  the 
husband  of  Mrs.  John  Smith. 

0)  No  cat  has  nine  tails  ;  one  cat  has  one  tail  more  than  no 
cat ;  therefore  one  cat  has  ten  tails. 

(/)  Keeping  a  promise  is  right;  Herod  kept  his  promise 
when  he  killed  John  the  Baptist ;  therefore  he  did  right. 

Qr)  Peter  is  a  saint;  therefore  his  denial  of  his  Lord  was  the 
act  of  a  saint. 

(//)  You  are  not  what  I  am  ;  I  am  a  man  ;  therefore  you  are 
not  a  man.  (J.) 

(/')  He  that  says  you  are  an  animal  speaks  truly  ;  he  that 
says  you  are  a  donkey  says  that  you  are  an  animal  ;  therefore 
he  speaks  truly. 

(/)  "Blessed  are  the  poor  in  spirit."  This  man  is  a  thief 
and  a  liar,  but  he  is  poor  in  spirit  ;  therefore  he  is  blessed. 

(/•)  It  is  a  well-recognized  maxim  that  the  king  can  do  no 
wrong.  Unless  the  maxim  is  false  it  was  not  wrong  for  the 
king  to  say  \vhat  he  did. 

(7)  He  who  is  most  hungry  eats  most;  he  \vho  eats  least  is 
most  hungry  ;  therefore  he  who  eats  least  eats  most.  (Aldrich.) 

(m}  Nuisances  are  punishable  bylaw;  a  noisy  dog  is  a  nui- 
sance ;  therefore  a  noisy  dog  is  punishable  by  law.  (D.) 

(;/)  Haste  makes  waste,  and  waste  makes  want ;  a  man  there- 
fore never  loses  by  delay. 

(o)  A  brick  house  is  cooler  than  a  frame  house  ;  therefore  this 
house  is  cooler  than  that  one. 

(  />)  Whatever  restricts  liberty  is  bad  ;  government  restricts 
liberty;  therefore  government  is  bad. 

(g)  Interference  with  another  man's  business  is  illegal ;  under- 
selling interferes  with  another's  business  ;  therefore  underselling 
is  illegal.  (D.) 

7.   Criticise  the  following  definitions: 

(u)  EQUIVOCATION  is  the  use  of  the  same  word  in  two 
different  senses  in  a  syllogism. 

(61)  A  FALLACY  OF  ACCIDENT  occurs  when  a  conclusion 
ab.iut  a  special  object  is  drawn  from  a  general  premise. 


EXERCISES.  435 

(£2)  From  a  general  to  a  special  case. 

(^3)  The  fallacy  of  accident  is  drawing  a  conclusion  concern- 
ing the  species  from  propositions  concerning  the  genus. 

(64)  Fallacy  of  accident  is  when  in  an  argument  you  go  from 
a  general  rule  to  a  special  case. 


CHAPTER  IV. 

1.  Criticise  the  following  divisions  : 

(n)  Human  beings  into  men,  women,  negroes,  boys,  females, 
and  cranks. 

(b)  Religions  into  true  and  false.     (C  ) 

(c)  Animals  into    bipeds,  quadrupeds,   birds,  monkeys,  and 
crawly  things. 

(of)  Quadrilateral  figures  into  squares,  rectangles,  parallelo- 
grams, and  rhomboids.  (F.) 

(e)  The  fine  arts  into  painting,  drawing,  sculpture,  architec- 
ture, poetry,  and  photography.  (F.) 

(/")  Governments  into  monarchies,  tyrannies,  oligarchies,  and 
democracies.  (F.) 

(g)  The  sciences  into  physical,  social,  ethical,  logical,  and 
metaphysical.  (F.) 

(/i)  Men  into  fools  and  knaves. 

(/)  Skin-diseases  into  those  that  are  cured  by  zinc  ointment 
and  those  that  are  not. 

2.  "  The  following  were  the  classes  of  persons  which  were  in 
1868  qualified  to  vote  in  one  or  other  of  the  United  States  of 
America:   Male  citizen,  male  inhabitant,  every  man,  white  male 
citizen,  white  freeman,  male  person,  white  male  adult,  free  white 
male  citizen,  free  white  man.    Forma  scheme  of  logical  division 
which  shall  have  a  place  for  each  of  the  above  classes."   (Jevons' 
"Studies  in  Deductive  Logic".) 

3.  Criticise  the  following  definitions: 

(rti)  GENUS  is  a  class  or  group  which  contains  all  the  funda- 
mental qualities  which  are  necessarily  possessed  by  the  species 
in  order  to  make  it  one  of  a  certain  genus. 

(a2)  A  genus  is  a  class  of  objects  made  up  of  a  collection 
of  other  classes,  these  objects  being  in  their  separate  classes 
because  of  common  characteristics. 

(03)  Genus  is  a  class  of  higher  objects. 


436  EXERCISES. 

(04)  Genus  is  a  class  made  up  of  several  specific  classes. 

(^5)  A  genus  is  a  name  applied  to  a  number  of  things  made 
up  of  several  (two  or  more)  species. 

(a6)  Genus  is  a  classification  of  objects  which  can  be  divided 
into  species.  It  is  the  largest  division  of  objects. 

(^7)  Genus  is  the  name  of  a  class  of  objects  which  may  be 
divided  into  species  and  subdivided. 

(aS)  Genus  is  a  name  of  a  class  of  objects  which  contain  two 
or  more  species. 

(«9)  Everything  is  a  species  of  some  larger  class  genus.  Thus 
genus  is  class  made  up  of  smaller  class  species. 

(b\)  SUMMUM  GENUS  is  the  largest  division  possible  of  a  cer- 
tain class  of  objects. 

(b2)  Summum  genus  is  the  greatest  of  all  genuses  in  exten- 
sion. 

(£3)  By  summum  genus  is  meant  highest  division  which 
can  be  made  according  to  any  given  basis.  For  instance,  on  a 
basis  of  intelligence,  man  is  the  summum  genus  of  living  beings. 

(&J.)  By  summum  genus  is  meant  the  highest  division,  i.e.,  the 
division  which  embraces  the  greatest  number  of  divisions  which 
may  be  subdivided,  e.g.,  Animal. 

(£5)  Summum  genus  or  genus  generalissimum  is  the  higher 
class  or  division  which  is  divided  into  species. 

(ci)  DIFFERENTIAE  are  the  attributes  of  the  individual  and 
not  common  to  the  class. 

(c2)  Differentiae  are  fundamenta  divisionis. 

(c^)  Differentiae  are  the  attributes  by  which  objects  or  classes 
of  objects  are  distinguished  from  each  other. 

(^4)  Differentiae  are  the  attributes  by  which  one  genus  differs 
from  another. 

(V5)  Differentiae  is  the  thing  upon  which  depends  the  putting 
or  leaving  out  an  object  from  a  class. 

(c6)  Differentiae  are  differences  which  objects  of  a  certain 
class  have  from  each  other. 

(/7)  Differentiae  is  the  name  given  to  the  difference  found  in 
the  attributes. 

(c8)  The  differentiae  of  a  word  or  object  express  the  difference 
between  the  object  and  the  class  to  which  it  belongs. 

(cf))  Differentiae  is  the  name  of  the  attributes  in  virtue  of 
which  a  species  is  subdivided. 

(<no)   Differentiae  are  the  attributes  which  must  be  known  to 


EXERCISES.  437 

distinguish  one  species  from  another  which  belongs  to  the  same 
genus. 

(<ni)  Differentiae  distinguish  the  species  of  the  genus. 

(c\2)  Differentia;  are  the  terms  by  which  one  object  is  dis- 
tinguished from  another. 

(</i)  ACCIDENT  is  that  quality  which  distinguishes  one  genus 
from  another. 

(1/2)  Accident  is  a  quality  which  belongs  to  the  class  genus, 
but  may  also  belong  to  some  other  class. 

(c/3)  Accident  is  a  quality  which  certain  terms  have  and  cer- 
tain other  terms  do  not. 

(c/4)  Accident  is  a  property  which  a  thing  may  or  may  not 
have  and  does  not  affect  the  class  to  which  the  thing  belongs. 

(</5)  An  accident  may  be  found  in  one  species  of  a  class  but 
not  necessarily  in  the  others. 

(</6)  Accident  is  that  which  may  be  true  of  one  object  of  a. 
class,  and  not  true  of  the  other  objects  of  that  class,  and  is  not 
needed  to  define  that  object. 

(dj)  An  accident  is  a  quality  which  belongs  to  an  object  per- 
manent or  temporary. 

(dS)  An  accident  is  a  relation  which  belongs  to  an  object 
temporarily  or  which  may  belong  to  that  particular  object,  on 
account  of  circumstances. 

(c/9)  An  accident  is  an  attribute  which  mayor  may  not  belong 
to  individual  members  of  the  same  species. 

(ei)  PROPERTY  is  a  term  applied  to  the  qualities  denoted  by 
the  term. 

f/2)  Property  is  a  quality  which  is  found  in  every  species  of  a 
genus. 

(/3)  Property  consists  of  the  quality  or  qualities  which  must 
be  added  to  the  species  to  make  it  a  genus. 

(c'4)  Property  is  a  quality  that  belongs  to  a  genus,  but  not 
one  for  which  the  genus  is  especially  known. 

(/5)  A  property  of  a  word  is  one  of  its  qualities. 

(^6)  Property  is  a  quality  or  qualities  which  an  individual 
must  possess  in  order  to  be  distinguished  from  any  other  indi- 
vidual. 

(ej)  A  property  of  a  term  is  something  that  belongs  to  it  but 
must  not  necessarily  be  included  in  the  definition. 

(fS)  Property  is  a  quality  that  belongs  to  every  member  of  a 
class. 


438  EXERCISES. 

(eg)  Property  is  a  quality  which  a  class  of  objects  may  possess, 
but  which  does  not  need  to  be  defined. 

(<?io)  Property  is  something  which  is  true  of  an  object,  but 
which  does  not  define  that  object. 

(^i  i)  Property  of  a  genus  or  species  is  a  quality  that  belongs 
to  that  genus  or  species  alone  and  distinguishes  it  from  all 
other  genera  and  species. 

(/i)  A  CROSS-DIVISION  is  the  classification  of  a  term  into  its 
genus  and  species. 

(/2)  Cross-division  is  where  the  word  may  belong  to  more 
than  one  species  at  once  and  these  different  species  cross  each 
other  and  make  it  difficult  to  get  any  good  order  out  of  them. 

(_/3)  In  making  a  division  of  a  class  of  things  or  genus  into 
species,  if  one  of  these  species  is  made  to  include  another  there 
is  a  cross-division. 

(_/4)  Cross-division  is  analysis  from  a  general  term  to  a  spe- 
cific, and  from  that  specific  used  as  a  general  term  to  its  specific, 
until  the  last  real  specific  can  be  found,  but  by  not,  in  one  or 
more  cases,  taking  the  next  specific  nearest  to  the  general  term. 

(f$)  Division  consists  in  placing  different  things  into  classes^, 
on    some   one  basis  of  division.     Cross-division  occurs   when 
division  is  made  on  two  or  more  bases. 


CHAPTER   V. 

1.  Consider  each  of  the  following  words  as  it  occurs  on  page 
217  and  determine  whether  it  is  a  term  or  not,  demonstrative  or 
descriptive,  connotative  or  non-connotative,  singular  or  general, 
collective  or  distributive,  abstract  or  concrete,  positive  or  nega- 
tive, relative  or  absolute  : 

Taxes,  Supporting,  The  church,  Party,  Fact,  The  forgotten 
man,  Woman,  Five,  Letters,  Corset-stitchers,  Seventy-five  cents, 
Machine,  Grade,  Prohibitory,  As,  To,  All,  Time,  Labor,  En- 
hancement, Price,  The  tax,  Best  terms,  Art,  Commerce,  To- 
dav. 

2.  Criticise  the  following  definitions  : 

(ai)  A  TERM  is  a  word  or  group  of  words  that  denote  a  quan- 
tity, state,  action,  or  relation  of  an  object  or  class  of  objects 
about  which  something  is  affirmed  or  denied. 

(a2)  Term  is  the  name  of  an  object  or  group  of  objects,  the 


EXERCISES.  439 

quality  or  action  or  condition  of  the  object  about  which  we  are 
thinking. 

(<*3)  A  term  is  the  name  of  an  object  or  group  of  objects  de- 
noting a  quality,  state,  action,  relation,  or  condition  about  which 
we  are  talking  or  thinking. 

(«4)  A  term  is  the  name  of  the  quality,  of  the  thought  of  the 
relation  of  the  thing  about  which  we  are  talking. 

(^5)  A  term  is  the  name  of  an  object  or  a  group  of  objects 
about  which  something  is  affirmed  or  denied. 

(a6)  A  term  is  the  name  of  a  state,  condition,  or  relation 
which  is  affirmed  or  denied  of  an  object. 

(aj)  A  term  is  the  name  of  a  quality,  relation,  or  state  under 
discussion.  In  a  proposition  the  subject  and  predicate  form  the 
two  terms. 

(aS)  A  term  is  a  name  of  an  object  about  which  we  are  think- 
ing, asserting,  or  questioning  some  relation,  quality,  or  con- 
dition. 

(bi)  A  GENERAL  TERM  is  one  that  npplies  to  all  the  objects 
belonging  to  the  class  to  which  the  term  applies. 

(b2)  A  general  term  is  one  in  which  all  the  objects  included 
under  a  given  general  name  are  designated. 

(^3)  A  general  term  is  one  applicable  to  each  of  a  certain 
number  of  similar  things. 

(b^)  A  general  term  is  one  which  distinguishes  a  particular 
class  of  individuals  as  such. 

(b^)  A  general  term  is  one  which  can  be  applied  to  any  one 
of  a  number  of  specified  individuals. 

(b6)  A  general  term  is  one  expressing  all  the  individuals  as 
such. 

(bj}  A  general  term  is  one  which  does  not  designate  an  aggre- 
gate of  similar  and  separable  things  considered  as  a  temporary 
unit. 

($8)  A  general  term  is  one  denoting  as  such  the  kind  of 
objects. 

(bg)  A  general  term  is  one  used  to  designate  a  class  of  objects 
which  are  not  separable. 

(bio)  A  general  term  is  one  which  designates  all  of  a  class  or 
group  of  objects. 

(ci)  A  SINGULAR  TERM  is  one  which  has  but  one  signification. 

(c2)  A  singular  term  is  one  used  to  apply  to  any  one  of  a  class 
of  objects. 


EXERCISES. 

1/5)  A  singular  term  is  one  which  points  to  one  specified  ob- 
ject or  class  of  objects. 

(c'4)  A  singular  term  is  a  name  applied  to  one  object  to  distin- 
guish it  from  the  other  objects  of  its  class. 

(<r5)  A  singular  term  is  one  which  is  applied  to  a  single  indi- 
vidual as  such. 

(c6)  A  singular  term  is  one  which  is  applied  to  a  singular  in- 
dividual as  such. 

(Y;)  A  singular  term  concerns  a  particular  individual  as 
such. 

(rS)  A  singular  term  is  one  expressing  a  specified  individual 
as  such. 

(eg)  A  singular  term  is  one  which  is  applied  to  a  particular 
designated  individual. 

(<rio)  A  singular  term  is  the  name  applied  to  a  certain  desig- 
nated object. 

(c\\)  A  singular  term  is  a  name  applied  to  a  certain  distin- 
guished object. 

(<ri2)  Singular  term  is  applied  purely  arbitrary  to  individuals. 

(cij)  A  singular  term  is  one  which  is  applied  to  a  certain  des- 
ignated object  and  no  other  iti  the  same  sense.  "This  man  is 
tall."  Man  is  a  singular  term. 

(Vi4>  A  singular  term  is  one  which  applies  to  only  one  indi- 
vidual or  object. 

(ti'i)  A  COLLECTIVE  TERM  is  a  term  made  up  of  individuals 
thought  of  as  separate  independent  objects. 

(</2)  A  collective  term  represents  a  number  of  singular  units 
taken  as  a  whole. 

(</3)  A  collective  term  is  a  term  applied  to  a  number  of  sim- 
ilar units,  as  in  case  of  a  mob. 

(</4)  A  collective  term  is  a  term  applied  to  a  group  of  indi- 
viduals. 

(</5)  A  collective  term  is  one  in  which  a  class  of  objects  taken 
as  a  whole  is  designated. 

(iK)  A  collective  term  is  one  applicable  to  a  whole  class  taken 
together. 

U/7)  What  is  said  of  a  collective  term  is  said  of  all  the  objects 
comprised  in  the  term  taken  as  a  whole. 

(<iS)  A  collective  term  is  one  which  may  be  applied  to  a  num- 
ber of  objects  taken  as  a  whole  on  the  ground  of  some  common 
likeness. 


EXERCISES.  441 

(</9)  A  collective  term  is  one  which  includes  a  number  of 
singular  terms. 

((ho}  A  collective  term  is  one  consisting  of  an  aggregate  of 
separable  and  single  individuals  considered  as  forming  some 
sort  of  temporary  unit. 

(dn)  A  collective  term  is  one  used  to  designate  a  group  of 
objects  which  may  be  separated. 

(/til)  A  collective  term  expresses  an  aggregate  of  a  "'imbcr 
of  similar  objects,  regarded  as  a  temporary  unit. 

(d\  3)  A  collective  term  is  one  which  can  be  applied  to  a  group 
of  specified  individuals  taken  as  one. 

(til 4)  A  collective  term  is  one  which  is  made  up  of  a  number 
of  similar  terms. 

(t'i)  A  DISTRIBUTIVE  TERM  is  one  which  expresses  univer- 
sality; as,  All  men  are  mortal.  All  men  is  distributive. 

(e"i)  A  distributive  term  is  one  which  includes  all  the  objects 
of  the  class  specified. 

(^3)  A  distributive  term  is  one  which  we  do  not  think  of  as 
being  made  up  of  a  number  of  similar  elements. 

((•4)  A  distributive  term  is  the  name  applied  to  a  number  of 
similar  objects  thought  of  as  a  whole. 

(^5)  A  distributive  term  is  a  name  applied  to  a  number  of 
objects  not  thought  of  as  separate,  individual,  simil.ir  tilings. 

(t'6)  A  distributive  term  is  a  name  applied  to  objects  thought 
of  as  made  up  of  a  number  of  similar,  separable,  and  indepen- 
dent elements. 

(^7)  A  distributive  term  indicates  some  of  the  objects  of  a 
class  as  such. 

(  f\)  An  ABSTRACT  TERM  is  one  which  expresses  an  indefinite 
relation  or  object,  such  as  disobedience  or  power. 

(_/2)  Abstract  has  in  it  the  idea  of  quality  and  attribute. 

(_/3)  Abstract  terms  are  nouns  which  express  some  sort  of 
relation. 

(_/4)  Abstract  term  is  that  which  is  not  the  name  of  matter 
but  expresses  an  active  relation. 

(_/5)  An  abstract  term  is  a  noun  which  involves  relations 
between  things  without  expressing  or  naming  them. 

(/6)  Abstract  signifies  a  quality,  act,  or  state  of  a  thing. 

(/"/)  An  abstract  term  is  one  which  cannot  be  thought  of 
without  its  relation  to  something  else  being  considered. 

(fS)  An  abstract  term  is  one,  used  in  a  grammatical  sentence, 


442  EXERCISES. 

which  does  not  necessitate  the  introduction   of  an   object  to 
which  it  is  applied  into  the  thought  of  the  proposition. 

(/9)  An  abstract  term  is  the  name  of  a  quality  not  involving 
the  mentioning  of  the  thing  itself. 

(fid)  Abstract  term  is  a  term  that  can  be  used  without  the 
object  being  mentioned  to  which  it  applies. 

(^i)  A  CONCRETE  TERM  is  an  adjective,  verb,  adverb,  or 
preposition  completing  the  meaning  of  a  verb. 

(gi)  Concrete  terms  are  names  of  things,  verbs,  adjectives, 
and  other  parts  of  speech. 

(g3)  Concrete  term  is  the  names  of  nouns,  adjectives,  and 
verbs. 

(//i)  A  RELATIVE  TERM  is  one  that  expresses  a  relation,  as 
father  and  son. 

(7/2)  A  term  may  be  relative  in  three  ways,  ist,  the  relation 
between  itself  and  an  invariable  standard;  2d,  the  comparison 
with  a  certain  variable  standard. 

(//3)  A  relative  term  is  one  whose  relation  with  another  term 
is  so  close  as  to  always  involve  the  apprehension  of  that  term 
as  a  part  of  a  larger  whole. 

(7/4)  Relative  term  is  one  that  expresses  one  party  of  a  rela- 
tion usually  active. 

(7/5)  Relative  term  is  one  which  denotes  relationship. 

(7/6)  If  the  standard  changes  when  the  same  term  is  applied 
to  different  things,  that  term  is  relative. 

(7/7)  Terms  are  relative  when  they  express  comparison  with  a 
variable  standard,  and  also  a  relation  between  two  objects 
which  are  mutually  dependent  in  meaning. 

(7^8)  Relative  terms  show  a  dependence  upon,  or  connection 
with,  some  other  term  or  object. 

(/i)  An  ABSOLUTE  TF.RM  is  one  which  expresses  quality  be- 
longing absolutely  to  that  object. 

(/2)  An  absolute  term  is  one  which  does  not  express  any 
relation. 

(/3»  If  the  standard  remain  the  same  when  the  same  term  is 
applied  to  different  things,  the  term  is  absolute,  i.e.,  perfect. 

(/4)  An  absolute  term  states  a  relation  between  things  re- 
ferred to  a  standard  which  does  not  vary. 

(/5)  An  absolute  term  is  one  stating  the  relations  of  the 
object  in  itself. 

The  CONNOTATION  of  a  word  is   the   special   meaning 


EXERCISES.  443 

which  it  conveys  to  the  mind  of  each  person  in  addition  to  the 
common  definition. 

(J2)  Connotation  is  the  significance  of  a  term  as  distin- 
guished from  others. 

(73)  The  connotation  of  a  term  are  the  attributes  belonging 
to  it. 

(/4)  Connotation  is  the  summing  up  of  all  the  attributes  of 
the  term  to  be  defined. 

(/5)  Connotation  is  the  consideration  of  attributes. 

(j6)  The  connotation  of  a  name  is  expressed  by  the  attributes 
by  virtue  of  which  the  name  is  applied. 

(_/7)  The  connotation  of  a  class  is  the  name  applied  to  the 
common  attributes  of  the  members  of  the  class,  by  virtue  of 
which  attributes  the  members  belong  to  the  class. 

(/8)  Connotation  is  the  relation  of  the  common  attributes  to 
the  general  term. 

(79)  The  connotation  of  a  name  is  the  concept  of  the  object 
designated  by  that  name. 

(;'io)  Connotation  is  the  enumeration  of  attributes  which  an 
object  must  have  in  order  to  be  known  by  the  general  name. 

(ji  i)  The  connotation  of  a  term  is  the  attribute  or  attributes 
vvhich  are  applied  to  the  object  about  which  you  are  speaking. 

3.  Give  the   exact   equivalent   of  the   following  in  concrete 
terms : 

(a)  Charity  never  faileth. 

(b)  Life  is  real,  life  is  earnest. 

(c)  Whether  we  realize   it   or  not,  our  lives  always  have  a 
moral  purpose. 

(d)  But  flesh  with  the  life  thereof,  which  is  the  blood  thereof, 
shall  ye  not  eat.     (Gen.  ix.  4.) 

(e)  He    stretcheth    out    the    north    over   empty    space,   and 
hangeth  the  earth  upon  nothing.     (Job  xxvi.  7.) 

(_/")  Our  demand  is  for  justice  to  silver  ! 

(g)  By  the  passes  which  he  made  he  drew  the  pain  from  the 
patient's  forehead  out  into  his  own  hands. 

(k)  The  energy  released  by  this  process  soon  travelled  from 
A  to  B  and  put  it  in  motion,  or  rather,  put  motion  into  it. 

(/)  Labor  is  oppressed  by  the  money  power. 

4.  Rewrite  these  paragraphs,  so  as  to  preserve  the  sense  but 
get  rid  of  as  many  of  the  abstract  terms  as  you  can.     In  the 
case  of  the  last  two  be  careful  to   interpret  the  words  as  the 


444  EXERCISES. 

author  meant  them  to  be  interpreted,  not  as  they  are  usually 
interpreted  nowadays. 

(a)  "  What    .  .  .    recommends    the    geometrical    method    to 
Spinoza  is,  not  only  its  apparent  exactness  and  the  necessity 
of  its  sequence,  but,  so  to   speak,  its  disinterestedness."     (Ed. 
Caird.) 

(b)  "  Men  generally  confound  this  distinction,  and  regard  all 
their  settled    opinions  or  beliefs  as    knowledge.     This    is    not 
merely  false,  but  absurd.  .  .   .  And  this  is  apparent  also  from 
the   nature  and  generation   of  our  opinions.     For,  in  general, 
these  come  to  us  not  from  any  conscious  process,  but  naturally 
and  spontaneously  from  many  sources,  as,  e.g.,  from  testimony, 
from  authority,  from  inaccurate  observation  or  careless  reason- 
ing, and  even   largely   from   mere    prejudice    or   bias.     Hence, 
familiar  to  us  as  our  opinions  are,  their  origin  in  general  is  as 
unknown  to  us  as  were  anciently  the  sources  of  the  Nile;  nor 
have  we  any  just  notion  of  the  grounds  on  which  they  rest,  or 
of  the  nature  and  justice  of  their  demands  on  our  belief.     Hence, 
until  some  means  of  verifying  our  opinions  be  found  and   ap- 
plied, we  can  have  no  assurance  of  their  rectitude.     The  first 
step  in  science  or  philosophy  must,  therefore,  be  to  distinguish 
between  verified  and  unverified  opinions.     The  former  consti- 
tutes true    knowledge  or  science  ;    the  latter — though  it  is  in 
fact  the  stuff  out  of  which  most  of    the  current  philosophy   is 
woven  —  has  no  just  pretension  to  the  name."      (G.  H.  Smith's 
"  Logic".) 

{c~]  "  Notwithstanding,  certain  it  is  that  if  those  schoolmen, 
to  their  great  thirst  of  truth  and  unwearied  travail  of  wit,  had 
joined  variety  and  universality  of  reading  and  contemplation, 
they  had  proved  excellent  lights,  to  the  great  advancement  of 
all  learning  and  knowledge;  but  as  they  are,  they  are  great 
undertakers  indeed,  and  fierce  with  dark  keeping:  but  as  in  the 
inquiry  of  the  divine  truth,  their  pride  inclined  to  leave  the 
oracle  of  God's  word,  and  to  vanish  in  the  mixture  of  their  own 
inventions;  so  in  the  inquisition  of  nature,  they  ever  left  the 
oracle  of  God's  works,  and  adored  the  deceiving  and  deformed 
images,  which  the  unequal  mirror  of  their  own  minds,  or  a 
few  received  authors  or  principles,  did  represent  unto  them.  ' 
Bacon,  "  Advancement  of  Learning",  Bk.  I. 

(d )  "  There  fall  out  to  be  these  three  distempers,  as  I  may 
term  them,  of  learning :  the  first,  fantastical  learning ;  the 


EXERCISES.  445 

second,  contentious  learning;  and  the  last,  delicate  learning; 
vain  imaginations,  vain  altercations,  and  vain  affectations ; 
and  with  the  last  I  will  begin.  Martin  Luther,  conducted  no 
doubt  by  a  higher  Providence,  but  in  discourse  of  reason  find- 
ing what  a  province  he  had  undertaken  against  the  Bishop  of 
Rome  and  the  degenerate  traditions  of  the  church,  and  finding 
his  own  solitude  being  no  ways  aided  by  the  opinions  of  his 
own  time,  was  enforced  to  awake  all  antiquity,  and  to  call 
former  times  to  his  succors,  to  make  a  party  against  the  present 
time.  So  that  the  ancient  authors,  both  in  divinity  and  in 
humanity,  which  had  long  time  slept  in  libraries,  began  gener- 
ally to  be  read  and  revolved.  This  by  consequence  did  draw  on 
a  necessity  of  a  more  exquisite  travail  in  the  languages  original, 
wherein  those  authors  did  write,  for  the  better  understanding 
of  those  authors,  and  the  better  advantage  of  pressing  and 
applying  their  words.  And  thereof  grew  again  a  delight  in 
their  mannerof  style  and  phrase,  and  an  admiration  of  that  kind 
of  writing,  which  was  much  furthered  and  precipitated  by  the' 
enmity  and  opposition  that  the  propounders  of  those  primitive 
but  seeming  new  opinions  had  against  the  schoolmen  ;  who 
were  generally  of  the  contrary  part,  and  whose  writings  were 
altogether  in  a  differing  style  and  form  ;  taking  liberty  to  coin 
and  frame  new  terms  of  art  to  express  their  own  sense,  and  to 
avoid  circuit  of  speech,  without  regard  to  the  pureness,  pleas- 
antness, and,  as  I  may  call  it,  lawfulness  of  the  phrase  or  word." 
Bacon,  loc.  cit. 

5.  'This  cheap  quack  thought  he  could  gull  the  public,  so  he 
put  some  dirty  water  in  a  bottle  and  then   turned  all  his  low 
cunning  to  the  invention  of  a  lying  advertisement  in  which  he 
claims  that  one  bottle  of  his  nasty  stuff  will   cure  a  man   of 
everything  under  the  sun  except  his  credulity.'     When  a  person 
makes  such   a  statement  as  this,  what  probably  are  the  ascer- 
tained facts  in  the  case  ? 

6.  Pick  out  the  demonstrative  and  the  descriptive  words  and 
phrases  in  the  following  : 

(a)  And  this  is  my  little  daughter  !  But  she  is  my  big  daugh- 
ter now. 

(b}  The  swift-footed  Achilles  is  lame. 

(c)  Smith  and  Jones,  manufacturers  of  Mrs.  Kelly's  home- 
made pickles. 

(ti)  Many  oriental  antiques  are  now  manufactured  in  Chicago. 


446  EXERCISES. 

7.  What  fallacy,  if  any,  is  to  be  found  in  the  following  ? 

(<?)  Books  are  a  source  both  of  instruction  and  amusement  ; 
a  table  of  logarithms  is  a  book ;  therefore  it  is  a  source  both  of 
instruction  and  amusement.  (J.) 

(b)  Three  and  two  are  two  numbers;  five   is  three  and  two; 
therefore  five  is  two  numbers.     (Ray.) 

(c)  I  hate  the  English  and  I  always  shall ;  for  was  it  not  they 
who  fought  against  us  in  the  Revolutionary  War  and  again  in 
1812? 

(a)  Unless  his  cold  works  out  through  the  throat  or  nose, 
how  can  he  hope  to  get  rid  of  it  ? 

(e)  Do  not  let  him  learn  all  those  useless  facts  ;  they  will  over- 
load his  mind. 

(_/)  You  say  that  A  is  taller  than  B  and  shorter  than  C  ;  but 
that  is  absurd,  for  the  same  person  cannot  be  both  taller  and 
shorter  at  the  same  time. 

(_£-)  It  is  all  very  well  for  you  to  talk  in  prayer-meeting  about 
•your  badness,  but  when  any  one  tells  you  outside  that  you  are 
bad  you  resent  it. 

(//)  The  people  of  the  country  are  suffering  from  famine  ;  and 
as  you  are  one  of  the  people  of  the  country  you  must  be  suffer- 
ing from  famine.  (J.) 

(/)  '  You  gave  him  all  the  information  lie  had  ! '  Then  you 
were  very  foolish  ;  for  you  had  none  too  much  for  yourself. 

(_/')  All  the  trees  in  the  park  make  a  thick  shade  ;  this  poplar 
is  one  of  them,  and  therefore  it  makes  a  thick  shade.  (J., 
altd.) 

(/£•)  It  is  true  that  in  a  democracy  the  people  vote,  but  it  is 
absurd  to  say  that  they  rule ;  for  you  and  I  are  people  and 
everything  we  vote  for  is  defeated. 

(I)  In  a  republic  a  majority  of  the  people  rules.  That  is  what 
we  mean  by  the  word.  Therefore  it  is  a  contradiction  to  say 
that  the  majority  of  the  people  did  not  rule  in  the  South  African 
Republic. 

(;«)  '  You  said  that  these  cakes  were  hot,  and  when  I  bought 
them  I  foand  that  they  were  frozen.'  'I  never  said  they 
were  hot;  I  simply  called:  Hot  cakes! — that  is  the  name  of 
them.' 

(«)  The  civilization  of  this  people,  like  every  other  organism, 
was  developed  gradually  from  small  beginnings  and  some  day 
it  is  bound  to  decay. 


EXERCISES.  447 

(a)  The  ancient  Greeks  produced  the  greatest  masterpieces  of 
eloquence  and  philosophy  ;  the  Lacedaemonians  were  ancient 
Greeks  ;  therefore  they  produced  the  greatest  masterpieces  of 
eloquence  and  philosophy.  (J.) 

(p)  We  shared  his  money  and  then  we  shared  his  sorrows  ; 
so  that  if  we  did  not  leave  him  very  much  of  the  former  we  did 
not  leave  him  much  of  the  latter  either. 

(q]  He  who  believes  himself  to  be  always  in  the  right  in  his 
opinion,  lays  claim  to  infallibility;  you  always  believe  yourself 
to  be  in  the  right  in  your  opinion  ;  therefore  you  lay  claim  to 
infallibility.  (W.) 

(r)  The  life  is  gone,  and,  since  there  are  no  vacant  places 
in  Nature,  something  has  come  to  take  its  place,  namely, 
death. 

(s)  No  soldiers  should  be  brought  into  the  field  who  are  not 
well  qualified  to  perform  their  part;  none  but  veterans  are 
well  qualified  to  perform  their  part  ;  therefore  none  but  vet- 
erans should  be  brought  into  the  field.  (W.) 

(/)  The  accumulated  experiences  which  we  inherit  from  our 
ancestors  have  always  shown  that  the  wages  of  sin  is  death. 

(«)  You  say  that  you  did  not  understand  that  this  move  was- 
contemplated  ;  and  yet  it  was  recommended  by  the  directors, 
and  you  are  one  of  them. 

(?/)  '  Love  my  neighbor  ! '  Yes.  But  that  is  no  reason  why 
I  should  not  get  ahead  of  one  of  these  soulless  corporations  if  I 
can. 

(w)  How  can  I  be  religious  when  religion  has  done  so  much 
harm  in  the  world  ?  What  makes  the  Mohammedans  so  intol- 
erant ?  WThat  makes  the  people  of  India  so  helpless?  What 
made  the  great  wars  of  history  ?  What  keeps  Ireland  and  Eng- 
land always  at  strife  ?  What  made  the  Inquisition  ?  What 
has  opposed  every  fundamentally  new  scientific  conception  for 
centuries  ?  Always  religion  ! 

(x}  "  No  reason,  however,  can  be  given  why  the  general  hap- 
piness is  desirable,  except  that  each  person,  so  far  as  he  believes 
it  to  be  attainable,  desires  his  own  happiness.  This,  however, 
being  a  fact,  we  have  not  only  all  the  proof  which  the  case  ad- 
mits of,  but  all  which  it  is  possible  to  require,  that  happiness  is 
a  good,  that  each  person's  happiness  is  a  good  to  that  person, 
and  the  general  happiness,  therefore,  a  good  to  the  aggregate 
of  all  persons."  (Mill's  "  Utilitarianism.") 


448  EXERCISES. 

(y)  "  Little  Indian,  Sioux  or  Crow, 

Little  frosty  Eskimo, 
Little  Turk  or  Japanee, 
O  !  don't  you  wish  that  you  were  me? 

You  must  often,  as  you  trod, 
Have  wearied  not  to  be  abroad. 
You  have  curious  things  to  eat, 
I  am  fed  on  proper  meat. 
You  must  dwell  beyond  the  foam, 
But  I  am  safe  and  live  at  home." 

(R.  L.  Stevenson.) 


CHAPTER  VI. 

T.  Take  O.  W.  Holmes'  "  Last  Leaf"  or  some  other  piece  of 
poetry  or  prose  and  show  the  relations  expressed  by  each  word 
or  phrase,  thus  : 

I  saw  him  once  before 
As  he  passed  by  the  door, 

And  again 

The  pavement  stones  resound, 
As  he  totters  o'er  the  ground 

With  his  cane. 

•  I  ' — individual  identity. 

'  Saw  ' — noetic  relation  ;  also  time  ;  also  perhaps  a  suggestion 
of  causation,  since  I  could  not  have  seen  him  unless  he  had 
acted  in  some  way  upon  me. 

'As  he  passed  by  the  door' — time;  also  causation  if  the 
phrase  implies  that  his  passing  the  door  was  what  made  me  see 
him.  'Passed  by  the  door' — motion;  i  e.,  change  of  place, 
involving  the  relations  of  both  time  and  place. 

'The  door' — individual  ideivity,  if  the  term  is  really  intended 
to  mean  the  movable  thing  that  we  use  to  close  an  aperture. 
In  this  case  the  word  also  suggests  the  complex  relation  of 
means  and  end  if  we  stop  to  think  about  it.  But  in  this  con- 
text the  term  is  more  probably  used  to  mean  the  open  doorway. 
If  this  be  so  the  relation  expressed  is  mainly  one  of  position 
in  space,  though  the  term  and  context  also  suggest  the  absence 


EXERCISES.  449 

of  a  causal  relation, — he  came  into  a  certain  position  where 
nothing  prevented  me  from  seeing  him. 

2.  Criticise  the  following  definitions  : 

(ui)  A  REAL  PROPOSITION  tells  the  name  of  the  object.  It 
does  not  tell  what  state  the  object  is  in. 

(d2)  A  real  proposition  asserts  something  of  a  term. 

(^3)  A  real  proposition  is  one  in  which  there  is  identity,  also 
description. 

[114]   Real  terms  relate  to  things. 

(175)  A  real  proposition  is  one  which  states  a  relation. 

(n6)  Real  propositions  state  some  additional  fact  about  an 
object. 

(1) \)  A  VERBAL  PROPOSITION  is  one  which  defines  an  object. 

(f'2)  A  verbal  proposition  is  one  which  explains  the  meaning 
of  nouns  or  the  terms  of  the  proposition. 

(7^3)  A  verbal  proposition  is  one  which  defines  an  object. 

(64)  A  verbal  proposition  is  the  mean  ing  of  a  name. 

(/>5)  Verbal  propositions  define  the  object  itself. 

(l>6)  A  verbal  proposition  is  one  which  explains  a  part  or  the 
whole  of  some  thing. 

(7>7)  A  verbal  proposition  explains  the  meaning  of  a  word 
within  the  proposition. 

(/>S)  Verbal  terms  relate  to  words. 

(t'jg)  A  verbal  proposition  explains  the  term  or  some  part 
of  it. 

2.  Consider  how  far  each  of  the  five  fundamental  relations 
given  in  the  text,  is  independent  of  the  others.  Is  it  possible, 
for  example,  for  anything  to  have  individual  identity  without 
also  being  the  subject  of  states,  and  vice  versa  ;  can  we  know  a 
thing  unless  it  acts  ;  can  a  thing  be  said  to  have  a  state  or  qual- 
ity unless  some  one  knows  it?  etc. 


CHAPTER   VIII. 

i.  What  is  the  subject,  what  is  the  copula,  and  what  is  the 
predicate  of  each  of  the  following  propositions  ;*  what  is  its 
quality  and  quantity  ;  and  if  the  predicate  has  any  quantity 
what  is  it?  If  the  proposition  is  ambiguous  or  peculiar  in  any 

*  Taken  for  the  most  part  from  the  collection  in  Jcvons's  "  Studies  in 
Deductive  Logic  ",  p.  38.  (Macmillan,  1884.) 


45°  EXERCISES. 

other  way,  point  out  the  fact ;  and  if  the  termc  are  abstract  make 
them  concrete. 

(«)  All  Athenians  are  Greeks. 

(t>)  They  never  pardon  who  have  done  the  wrong. 

(f)  Great  is  Diana  of  the  Ephesians. 

(d)  No  abracadabras  are  gasteropods. 

(e]  All,  all  are  gone,  the  old  familiar  faces. 
(/)  He  that  is  not  for  us  is  against  us. 

(g)  Men  mostly  hate  those  whom  they  have  injured, 
(/z)  Old  age  always  involves  decrepitude. 

(/)  Nothing  morally  wrong  is  politically  right. 
(j)  It  is  not  good  for  man  to  be  alone. 
(k)  A  certain  man  had  two  sons. 

(/)  There's  something  rotten  in  the  state  of  Denmark. 
(m)  All  cannot  receive  this  saying. 
(«)  Few  men  are  free  from  vanity. 

(<?)  He  that  fights  and    runs  away  may  live  to  fight  another 
day. 

(/>)  There  is  none  good  but  one. 

(g)  Two  straight  lines  cannot  enclose  a  space. 

(r)  Familiarity  breeds  contempt. 

(v)  Only  the  ignorant  affect  to  despise  knowledge. 

(/)  All  is  not  gold  that  glitters. 

(u)  Love  is  not  love  which  alters  when  it  alteration  finds. 

(?)  A  friend  should  bear  a  friend's  infirmities. 

2.  '  Few  books  are  at  once  learned  and  amusing.'     This  is 
treated  in  the  passage  quoted  from  Jevons  on  p.  98  as  proposi- 
tion O.     Consider  whether  it  might  be  regarded  as  equivalent 
to  both  O  and  I,  or  to  an  exclusive  or  exceptive  proposition. 

3.  Give    hypothetical  and  disjunctive  equivalents  for  all  the 
universal  propositions  in  the  first  exercise  on  this  chapter. 

4.  Are  the  following  propositions  disjunctive  or  hypothetical  ? 
Give  their  categorial  equivalents;  also  their  exclusive  and  ex- 
ceptive equivalents. 

(ii)  If  you  are  a  man  you  are  mortal. 

(b~)   Either  you  are  a  man  or  you  are  mortal. 

(c)  Either  you  are  a  man  or  you  are  not  mortal. 

(d)  If  you  are  not  mortal  you  are  a  man. 

(e)  You  will  not  go  to  heaven  unless  you  are  good. 
(/)  You  will  not  go  to  hell  if  you  are  not  bad. 

5.  When  I  say  'No  men  are  infallible  '  how  many  men  am  I 


EXERCISES.  451 

talking  about  ?     When    I  say  '  All  men  are  not  infallible  '  how 
many  am  I  talking  about  ? 

6.  Examine,  and  if  necessary  correct,  the  statement  on  p.  102 
that  'Almost  any  Turk  hates  a  Greek'  is  universal  with  refer- 
ence to  the  Greeks. 

7.  Criticise  the  following  definitions: 

(ai)  SINGULAR  PROPOSITION  denotes  an  individual  as  such. 

(112)  A  singular  proposition  is  one  which  specifies  a  single 
one  of  several  relations. 

(^3)  A  singular  proposition  is  one  in  which  singular  terms 
are  used. 

(«4)  A  singular  proposition  is  one  which  deals  with  or  treats 
of  a  singular  term. 

(«5)  A  singular  proposition  is  one  which  makes  a  statement 
about  some  one  of  a  class  of  objects  not  especially  designated. 

(d6)  A  singular  proposition  is  applicable  to  certain  designated 
members  of  a  class  as  such. 

(a"])  A  singular  proposition  is  one  that  states  something 
about  certain  designated  members  of  a  class. 

(<*S)  A  singular  proposition  is  one  that  makes  a  statement 
about  an  individual  object. 

(in))  Singular  proposition  is  one  in  which  we  find  certain 
specified  objects  pointed  out. 

(<no)  Singular  proposition  is  one  which  states  something 
about  an  individual  and  leaves  no  doubt  as  to  whether  it  is 
referring  or  is  meant  to  refer  to  a  tiling  or  is  applicable  or 
meant  to  apply  to  a  thing. 

('in)  A  singular  proposition  is  one  which  refers  to  certain 
specified  individuals  and  leaves  no  doubt  as  to  who  is  under 
discussion. 

(l>\)  UNIVERSAL  PROPOSITION  is  one  in  which  the  predicate 
is  affirmed  of  the  whole  subject. 

(b2)  A  universal  proposition  is  one  which  distributes  its  sub- 
ject but  not  its  predicate. 

(/>3)  Universal  propositions  are  those  which  involve  state- 
ments about  all  the  objects  included  in  the  subject  term. 

(l>4)  Propositions  are  universal  when  they  make  statements 
about  all  the  objects  mentioned  in  the  subject  term. 

(£5)  A  universal  proposition  is  a  statement  which  affirms  or 
denies  something  about  all  the  objects  in  the  class  to  which  the 
subject  term  belongs. 


45 2  EXERCISES. 

(b6)  A  universal  proposition  is  one  in  which  a  statement  is 
made  of  some  particular  object  definitely  specified. 

(by)  Universal  as  applied  to  a  proposition  is  the  quality  of 
embracing  all  of  the  objects  belonging  to  the  class  specified  in 
the  subject  of  the  proposition. 

(38)  A  universal  proposition  is  one  in  which  an  affirmation  is 
made  concerning  every  object  of  the  kind  denoted  by  the  sub- 
ject term. 

(^9)  A  proposition  is  universal  when  the  statement  made  is 
true  of  every  object  indicated  by  the  subject  term. 

(bio)  Universal  as  applied  to  propositions  refers  to  all  the 
objects  indicated  by  the  subject  term. 

(ii)  A  PARTICULAR  PROPOSITION  is  one  which  has  for  its 
subject  a  singular  term. 

(c2)  A  particular  proposition  is  one  whose  predicate  does  not 
apply  to  all  of  the  subject. 

(c$)  A  particular  proposition  is  one  in  which  the  predicate  is 
stated  of  part  of  the  subject. 

(£4)  A  particular  proposition  is  one  in  which  the  predicate  is 
not  affirmed  or  denied  of  all  the  subject. 

(r,)  A  particular  proposition  is  one  which  makes  an  assertion 
about  an  indefinite  part  of  a  subject. 

(r6)  A  particular  proposition  is  one  in  which  the  predicate 
affirms  or  denies  only  a  part  of  an  indefinitely  designated  group 
of  objects. 

(c~)  A  particular  proposition  is  one  in  which  a  statement  is 
made  concerning  a  part  of  an  indefinite  number  of  objects. 

(rS)  A  particular  proposition  is  one  that  asserts  something  of 
an  indefinite  number  of  objects. 

(eg)  A  particular  proposition  is  one  in  which  the  predicate 
makes  a  statement  about  any  part  of  the  thing  talked  about. 

(no)  A  particular  proposition  is  one  which  does  not  make  a 
statement  about  all  of  a  class  of  objects,  but  about  some  par- 
ticular member  of  a  class. 

(i'i  i )  A  particular  proposition  is  a  proposition  which  has  a 
subject  which  does  not  include  a  whole  class,  but  onlv  some. 

(c-'i2)  A  particular  proposition  is  one  in  which  a  statement  is 
made  regarding  some  portion  of  the  class  of  objects  designated 
by  the  subject  of  the  proposition. 

(iti)  The  OUANTITY  of  a  proposition  refers  to  the  fact  whether 
it  is  negative  or  affirmative. 


EXERCISES.  453 

(</2)  Quantity  is  the  character  of  a  proposition  which  states 
whether  it  is  singular,  universal,  or  particular. 

(//3)  The  quantity  of  a  proposition  is  its  form  as  to  whether  it 
affirms  something  about  the  whole  of  a  subject  or  something 
about  undesignated  members;  in  other  words,  whether  it  is  uni- 
versal, particular,  or  singular. 

(</4)  Quantity  is  the  affirmation  or  denial  of  a  thing  as  uni- 
versal or  particular. 

(</5)  Quantity  is  that  character  of  a  proposition  as  distin- 
guishing the  universal  from  the  particular. 

(d6)  The  quantity  of  a  proposition  is  that  property  of  a  prop- 
osition by  which  a  proposition  is  considered  as  universal,  re- 
ferring to  all  of  a  class,  singular,  referring  to  some  specified 
part  of  a  class,  or  particular,  referring  to  some  unspecified  part 
of  a  class. 

(dj)  Quantity  has  reference  to  the  kind  of  propositions, 
whether  they  be  universal  or  singular,  as  distinguished  from 
other  kinds. 

(d&)  Quantity  is  that  characteristic  of  a  proposition  which 
marks  it  as  universal,  particular,  singular,  or  indefinite. 

(</9)  Quantity  is  the  character  of  a  proposition  which  states 
something  about  all  the  members  of  a  class,  undesignated  mem- 
ber or  members,  or  a  specified  individual  or  member. 

(ei)  AN  AFFIRMATIVE  PROPOSITION  is  one  in  which  the  pred- 
icate affirms  or  asserts  something  about  the  subject. 

(<?2)  An  affirmative  proposition  is  one  where  a  certain  rela- 
tion is  said  to  exist  between  the  subject  and  predicate. 

(^3)  An  affirmative  proposition  is  one  which  expresses  a  cer- 
tain agreement  between  the  subject  and  predicate  so  that  the 
qualities  of  the  predicate  belong  to  the  subject. 

(^4)  An  affirmative  proposition  is  one  which  tells  some  fact 
about  the  object  named  in  the  subject. 

(t'5)  An  affirmative  proposition  is  a  statement  of  a  fact  and 
whose  predicate  refers  to  the  name  of  the  subject. 

(t-6)  An  affirmative  proposition  is  one  which  makes  a  positive 
assertion. 

(ej)  An  affirmative  proposition  is  one  which  asserts  the  predi- 
cate as  having  qualities  belonging  to  the  object  which  the  sub- 
ject represents. 

(e8)  An  affirmative  proposition  is  one  which  affirms  a  certain 
relation  or  condition  between  two  terms. 


454  EXERCISES. 

(^•9)  An  affirmative  proposition  is  one  in  which  the  predicate 
is  asserted  to  belong  to  either  the  whole  subject  or  a  part  of  the 
subject. 

(eio)  An  affirmative  proposition  is  one  in  which  the  qualities 
of  the  predicate  are  asserted  as  belonging  to  the  subject. 

(/')  QUALITY  has  to  do  with  whether  a  proposition  is  sin- 
gular, particular,  or  universal. 

(f2)  Propositions  are  said  to  differ  in  quality  when  they  are 
affirmative  or  negative. 

(/3)  Propositions  differ  in  quality  when  one  affirms  and  the 
other  denies  a  statement. 

(/4)  The  quality  of  a  proposition  indicates  whether  it  is 
affirmative  or  negative. 

( /5)  The  quality  of  a  proposition  is  in  regard  to  its  nature  as 
affirmative  or  negative. 

(f6)  The  quality  of  a  proposition  is  the  relation  between 
A  E  I  O. 

(/7)  The  quality  of  a  proposition  is  the  attribute  or  attributes 
of  the  subject  term  taken  together. 

(fS)  The  quality  of  a  proposition  is  the  character  of  a  propo- 
sition as  it  affirms  or  denies. 

(/9J  Quality  as  applied  to  propositions  is  that  attribute  of 
the  proposition  which  determines  whether  the  proposition  is 
affirmative  or  negative. 

(/io)  The  quality  of  a  proposition  is  its  character  as  to  the 
affirmation  or  negation  of  the  statement  made  in  the  proposition. 

(/i  i)  Quality  of  a  proposition  is  its  form  as  to  whether  it  is 
affirmative  or  negative. 

( ifi)  A\r  KXCKPTIVE  PROPOSITION  affirms  or  denies  some- 
thing of  an  object  mentioned. 

(^2)  In  an  exceptive  proposition  something  is  affirmed  or 
denied  of  the  object  excluded. 

(gj)  An  exceptive  proposition  refers  to  some  unspecified 
objects. 

(i/4)  An  exceptive  proposition  is  one  in  which  something  is 
affirmed  or  denied  of  some  part  of  the  subject  specified. 

(1/5)  Exceptive  propositions  are  those  which  affirm  the  predi- 
cate of  all  the  subject  except  certain  well-defined  cases  to  which 
the  subject  does  not  belong. 

( g£>)  An  exceptive  proposition  is  one  that  states  something 
about  all  specified  members  of  a  class  except  certain  ones. 


EXERCISES.  455 

(g7~)  An  exceptive  proposition  is  one  that  states  something 
about  all  but  the  unspecified  member  or  members  of  a  class. 

( g8)  Exceptive  term  as  applied  to  propositions  is  used  to 
mean  that  the  predicate  affirms  the  subject  in  all  cases  with  one 
exception. 

(//i)  AN  EXCLUSIVE  PROPOSITION  affirms  or  denies  some- 
thing of  an  object  not  mentioned. 

(hi)  An  exclusive  proposition  is  one  in  which  something  is 
told  about  the  individuals  specified  in  the  subject  term. 

(//•})  An  exclusive  proposition  is  one  which  tells  something 
about  a  designated  part  of  the  subject  term. 

(//4)  An  exclusive  proposition  is  one  which  denies  the  truth 
or  falsity  of  a  part  of  the  object  spoken  of. 

//5)  An  exclusive  proposition  states  something  about  certain 
specified  members  of  a  class. 

(//6j  An  exclusive  proposition  is  one  which  states  something 
only  about  a  specified  member  of  a  class. 

(7/7)  An  exclusive  proposition  uses  the  words  "  only  ",  "  none 
but  "  in  asserting  the  predicate  of  the  subject. 

(//S)  An  exclusive  proposition  is  the  statement  of  one  of  a 
class  to  the  exclusion  of  all  other  members  of  that  class. 

8.  Criticise  the  following  arguments  : 

(L?)  Every  lover  of  truth  is  an  admirer  of  Huxley;  every 
bishop  in  the  established  church  is  not  ;  therefore  the  bishops 
of  the  established  church  are  not  lovers  of  truth. 

(b)  Those  who  have  sacrificed  their  health  and  fortune  for  a 
principle   deserve   the   gratitude   of   mankind ;    few  men    have 
done  this;  therefore  few  men  deserve  the  gratitude  of  mankind. 

(c)  All   poets   are    not    imaginative;    some    philosophers  are 
poets  ;  therefore  some  philosophers  are  not  imaginative.     (Ray.) 

(if)  The  Cretans  are  liars;  A,  B,  C  are  Cretans;  therefore 
A,  B,  C  are  liars.  (Hamilton.) 

(i')  All  that  glitters  is  not  gold  ;  tinsel  glitters  ;  therefore  it  is 
not  gold.  (W.) 

(_/ )  Warm  countries  alone  produce  wines ;  Spain  is  a  warm 
country  ;  therefore  Spain  produces  wines.  (W.) 

(.4')  Revenge,  Robbery,  Adultery,  Infanticide,  etc.,  have  been 
countenanced  by  public  opinion  in  several  countries;  all  the 
crimes  we  know  of  are  Revenge,  Robbery,  Adultry,  Infanticide, 
etc.  ;  therefore  all  the  crimes  we  know  of  have  been  coun- 
tenanced by  public  opinion  in  several  countries.  (W.) 


45 6  EXERCISES. 

(//)  The  learned  are  pedants;  A  is  a  learned  man;  therefore 
A  is  a  pedant.  (Ray,  quoted.) 

(/)  Testimony  is  a  kind  of  evidence  which  is  very  likely  to 
be  false  ;  the  evidence  on  which  most  men  believe  that  there 
are  pyramids  in  Egypt  is  testimony  ;  therefore  the  evidence  on 
which  most  men  believe  that  there  are  pyramids  in  Egypt  is 
very  likely  to  be  false.  (W.) 

(_/)  All  the  miracles  of  Jesus  would  fill  more  books  than  the 
world  could  contain  ;  the  things  related  by  the  Evangelists  are 
the  miracles  of  Jesus ;  therefore  the  things  related  by  the 
Evangelists  would  fill  more  books  than  the  world  could  con- 
tain. (W.) 

(/')  No  trifling  business  will  enrich  those  engaged  in  it  ;  a 
mining  speculation  is  no  trifling  business  ;  therefore  a  mining 
speculation  will  enrich  those  engaged  in  it.  (W.) 

(/ )  Every  Turk  hates  a  Greek  ;  Dr.  Constantinides  is  a  Greek  ; 
therefore  every  Turk  hates  Dr.  Constantinides. 

(in)  The  English  and  Germans  are  quarrelling;  I  am  English 
and  you  are  German ;  therefore  you  and  I  are  quarrelling. 

CHAPTER    IX. 

irt.  Assume  the  truth  of  each  in  turn  of  the  propositions 
A,  E,  I,  O,  Singular  Affirmative  and  Singular  Negative,  and 
inquire  what  follows  in  each  case  about  the  truth  or  falsity  of 
the  others. 

\b.  Assume  the  falsity  of  each  in  turn  of  these  propositions 
and  inquire  what  follows  about  the  truth  or  falsity  of  the  others. 

2.  If  you  wish  to  put  an  opponent  in  the  wrong,  what  kind  of 
statements  should  you  try  to  get  him  to  make,  and  what  kind 
of  statements  should  you  yourself  try  to  avoid  making  ? 

3<z.  '  None  but  the  strong  survive.'  Resolve  this  into  two 
ordinary  propositions. 

•^b.  Make  a  list  of  all  the  propositions  with  which  it  is  incon- 
sistent, and  from  these  pick  out  its  contradictory. 

4.  Find  the  contradictory  or  contradictories  of  the  following  : 
'If  a  person   is  a  good  citizen,  he   will  not  smuggle',  'Heavy 
objects  do  not  necessarily  fall  when  they  are  thrown  into  the 
air.' 

5.  Estimate  the  truth  of  the  following  statements  and  correct 
them  if  they  are  wrong. 


EXERCISES.  457 

(a)  If  one  proposition  is  true,  then  any  other  proposition  from 
which  it  follows  is  true  also,  and  if  the  proposition*  in  question 
is  false,  then  the  other  from  which  it  follows  is  false  also. 

(&)  If  one  state  of  affairs  exists,  then  any  other  state  of  affairs 
which  its  existence  involves  exists  also,  and  if  the  first  state  of 
affairs  does  not  exist,  neither  does  the  other. 

(f)  If  the  truth  of  A  involves  the  truth  of  B,  and  the  falsity 
of  B  involves  the  falsity  of  A,  then  the  falsity  of  A  must  also 
^involve  the  falsity  of  B,  and  the  truth  of  B  .the  truth  of  A. 

6.  What  in  each  case  is  the  smallest  amount  of  information 
necessary  to  disprove  the  following  ? — 

(a)  Great  men  are  always  large  of  stature. 

(b)  Lazy  people  are  never  useful. 

(c)  A  certain  celebrated  statesman  died  in  a  lunatic  asylum. 
(it)  Some  dogs  are  afraid  of  ghosts. 

7.  Criticise  the  following  definitions  : 

(ai)  OPPOSITION  of  propositions  occurs  when  one  is  false 
and  the  other  true. 

(ti2)  Opposition  of  propositions  is  the  name  applied  to  the 
process  by  which,  taking  a  given  proposition  as  true,  we  deter- 
mine the  truth,  falsity,  or  doubtfulness  of  the  other  propositions. 

(l>i)  The  term  'CONTRADICTORY*  as  applied  to  propositions 
means  that  in  one  proposition  a  statement  cannot  be  both 
affirmed  or  denied  in  regard  to  a  certain  object. 

(b2)  A  contradictory  proposition  is  one  in  which  the  absence 
of  something  is  affirmed  or  denied  whose  presence  was  denied 
or  affirmed  in  the  original  proposition. 

(^3)  Contradictory  propositions  are  those  which  differ  either 
in  quantity  or  in  quality  or  in  both. 

(i>4)  Term  contradictory  as  applied  to  propositions.  A  nega- 
tive particular  proposition  is  the  contradictory  of  a  positive 
general. 

(£5)  A  contradictory  proposition  is  one  which  affirms  or 
denies  the  falsity  or  truth  of  the  proposition  with  which  it  is 
compared. 

(b6)  Contradictory  propositions  are  those  which  differ  in  both 
quantity  and  quality. 

(bj)  Two  propositions  are  contradictory  when  they  make 
statements  opposite  in  meaning. 

(68)  Contradictory  propositions  are  two  propositions  which 
cannot  both  be  true  at  the  same  time. 


458  EXERCISES. 

(^9)  A  contradictory  proposition  is  one  in  which  one  state- 
ment is  true  and  the  other  false. 

(bio)  Statements  are  said  to  be  contradictory  when  one 
affirms  and  the  other  denies  in  any  way  a  certain  thing  said 
about  an  object. 

(b\i)  When  we  have  one  proposition  which  is  universal 
affirmative  and  one  which  is  particular  negative,  these  two 
propositions  are  contradictory.  Or  if  we  have  a  universal  neg- 
ative and  a  particular  affirmative,  they  are  contradictory.  That 
is,  when  we  have  two  propositions  such  that  when  one  is  true 
the  other  must  be  false,  they  are  called  contradictory. 

(ci)  CoN'TRARY  propositions  are  those  which  directly  refute 
each  other.  If  one  is  true,  the  other  is  false. 

(cz)  Two  propositions  are  contrary  when  one  is  in  the  uni- 
versal affirmative  form  and  the  other  in  particular  negative 
form. 

(c^)  Contrary  propositions  are  those  which  assert  the  utmost 
variety  of  circumstances. 

(r4)  Contrary  propositions  are  those  in  which  there  is  a  con- 
trary relation  expressed,  as,  '  Wretched  people  are  unfortunate  ' 
is  the  contrary  proposition  of  '  Happy  people  are  fortunate'. 

(<:$)  Contrary  propositions  are  those  which  deny  a  state  of 
things  asserted  by  a  previous  proposition. 

(c6)  Contrary  propositions  are  those  in  which  what  is 
affirmed  of  all  the  subject  or  some  of  the  subject  in  one  propo- 
sition is  denied  of  all  the  subject  or  some  of  the  subject  in  the 
other  proposition. 

(/7)  A  universal  negative  and  a  universal  affirmative  are  called 
contrary  propositions  ;  one  is  false  and  one  is  true. 

(c&)  Contrary  propositions  are  propositions  which  are  di- 
rectly opposite  in  quality. 


CHAPTER   X. 

i.  Explain  the  following  so  as  to  make  clear  in  each  case 
what  relation  (cause,  motive,  premise,  law)  is  indicated  by  the 
italicized  words : 

(<0    Why  did  you  go  to  London  ?     (W.) 

(/;)    Why  is  this  prisoner  guilty  ?     (W.) 

(c)    Why  does  a  sto.->e  fall  to  the  earth  ?     (W.) 


EXERCISES.  459 

(d)    Why  do  the  germs  of  diphtheria  do  so  much  harm  ? 

(c)  This  ground  is  rich  because  the  trees  on  it  are  flourishing. 
(W.) 

(/)  The  trees  flourish  because  the  ground  is  rich.     (W.) 

(^')  "He  that  is  of  God  heareth  God's  words:  ye  therefore 
hear  them  not,  because  ye  are  not  of  God."  John  viii.  47. 

(h)  "  Why  do  ye  not  understand  my  speech?  Even  because 
ye  cannot  hear  my  word."  John  viii.  43. 

(/)  "  And  because  I  tell  you  the  truth,  ye  believe  me  not." 
John  viii.  45. 

(j)  "  And  no  man  laid  hands  on  him  ;  for  his  hour  was  not 
yet  come."  John  viii.  20. 

(/c)  "  And  ye  will  not  come  to  me  that  ye  might  have  life." 
John  v.  40. 

(/)  "  How  can  ye  believe,  which  receive  honour  one  of  an- 
other, and  seek  not  the  honour  which  cometh  from  God  only?  " 
John  v.  44. 

(in)  Two  cerebral  centres  once  connected  tend  to  keep  that 
^connection,  since  we  tend  to  have  the  same  thoughts  again  that 
we  have  had  before. 

2.  Obvert  the  following : 

(a}  This  writer  is  inconsistent. 

(/')  The  authors  of  these  books  are  specialists. 

(c)  Good  for  this  date  only. 

(it)  We  have  met  the  enemy  and  they  are  ours. 

(c)  I  was  not  alone. 

(/)  This  is  not  the  worst  filter  in  the  market. 

(if)  It  was  not  a  bad  dinner. 

(//)  It  is  not  unreasonable  to  suppose  that  a  man  with  all  his 
experience  and  all  his  success  would  be  abundantly  able  to 
perform  so  simple  a  task. 

(/)  The  luxuriousness  of  the  trees  is  not  the  cause  of  the 
soil's  fertility. 

(_/)  This  man  is  my  brother. 

(/t)  We  climbed  the  mountain. 

3.  Criticise  the  following  definitions  : 

(a)  OBVERSION  is  the  affirming  or  denying  of  a  statement 
which  has  previously  been  denied  or  affirmed. 

(6)  An  obverse  proposition  is  one  which  denies  or  affirms 
what  has  been  previously  affirmed  or  denied  and  vice  versa. 

(c)   Obversion  consists  in  affirming  or  denying  the  absence  of 


460  EXERCISES. 

qualities  whose  presence  has  been  affirmed  or   denied  in   the 
original  proposition. 

(//)  In  obversion  the  same  subject  is  kept,  but  that  is 
affirmed  or  denied  of  the  opposite  of  that  which  was  denied  or 
affirmed  in  the  previous  proposition. 

(e)  Obversion  is  the  moving  of  the  sign  of  negation  from  the 
copula  to  the  predicate  or  from  the  predicate  to  the  copula. 

(_/)  Obversion  is  making  a  proposition  include  all  it  excluded 
before  and  vice  versa. 

CHAPTER  XI. 

1.  Apply  the  traditional  conversion  to  all  the  propositions  in 
the  first  exercise  to  Chapter  VIII. 

2.  Obvert  each  of  the  following,  convert  what  you  get,  and 
keep  on  alternately  obverting  and  converting  until  you  cannot 
go  any  further.    Do  the  same  again,  beginning  with  conversion. 

(a)  All  good  children  are  happy. 

(b)  No  abracadabras  are  hypotheses. 

(f)  "  Who  noble  ends  by  noble  means  obtains 

Or,  failing,  smiles  in  exile  or  in  chains,  .   .  . 

That  man  is  blest  indeed." 
(d)  He  is  not  happy  who  is  dead. 

3.  If  it  is  not  true  that  John  is  no  heavier  than  James,  what 
can  we  say  about  James,  things  heavier  than  James,  things  not 
heavier  than  James,  things  heavier  than  John,  things  not  heav- 
ier than  John,  and  the  relation  'heavier'? 

4.  What  is  the  relation  of  opposition,  conversion,  and  obver- 
sion between  each  two  of  the  following  propositions  ? — 

(a)   All  the  trout  are  in  this  pond. 

(/;)  The  fish  in  the  other  pond  are  not  trout. 

(<:)   Some  of  the  fish  in  this  pond  are  not  trout. 

5.  Give  (a)  the  converse  of  the  obverse,  and  (b)  the  obverse  of 
the  converse  of  this  proposition  :   Every  pig  has  a  cloven  hoof. 
Then  apply  conversion  by  negation  to  the    resulting  proposi- 
tions. 

6.  Criticise  the  following  definitions: 

(a)  CONVKKSION  is  telling  something  in  a  new  proposition 
about  objects  predicated  in  another  proposition. 

(l>)  The  conversion  of  a  proposition  is  when  the  subject  and 
predicate  change  places. 


EXERCISES.  461 

(c)  The  converse  of  a  proposition  is  one  in  which  the  predi- 
cate is  taken  for  the  subject  and  the  subject  for  the  predicate. 

(d)  Conversion  is  saying   something   in  a    new   proposition 
about  the  objects  that  were  or  might  have  been  indicated  by 
the  predicate  of  the  original  proposition. 

7.  Criticise  the  following  arguments: 

(a)  None  but  the  industrious  deserve  to  succeed  ;  I  am  indus- 
trious ;  therefore  I  deserve  to  succeed. 

(b)  None  but  the  industrious  deserve  to  succeed  ;  I  deserve 
to  succeed  ;  therefore  I  am  industrious. 

(V)  The  express  train  alone  does  not  stop  at  this  station; 
and  as  the  last  train  did  not  stop  it  must  have  been  the  express 
train.  (J.) 

(it)  When  we  hear  that  all  the  righteous  people  are  happy,  it 
is  hard  to  avoid  exclaiming,  What  !  are  all  the  unhappy  per- 
sons we  see  to  be  thought  unrighteous  ?  (J.) 

(e)  All  equilateral  triangles  are  equiangular,  and  consequently 
all  equiangular  triangles  must  be  equilateral.     (F.) 


CHAPTER   XII. 

1.  Estimate  the  correctness  of  the  following  statements  : 

(a)  No  inference  can  be  drawn  unless  two  objects  are  com- 
pared with  a  third. 

(b)  No  inference  can  be  drawn  if  any  of  the  relations  in  ques- 
tion are  heterogeneous. 

2.  Criticise  the  following  definitions  : 

(a)  MEDIATE  inference  is  inference  drawn  from  more  than 
two  statements. 

(6)  Mediate  inference  is  an  inference  which  requires  a  middle 
term. 

(c)  Mediate  inference  is  inference  from  a  set  state  of  affairs— 
under  specific  conditions. 

(it)  In  mediate  inference  the  mind  has  more  than  one  act  to 
perform.  It  arrives  at  the  conclusion  by  means  of  other  state- 
ments than  just  the  one  in  regard  to  which  the  inference  is 
made.  Mediate  inference  is  used  chiefly  in  syllogisms. 

(«•)  Mediate  inference  is  reasoning  from  one  premise  to  an- 
other by  means  of  an  intervening  constructive  process. 

(f)  Mediate  inference   is  that  form  of  reasoning  which  re- 


462  EXERCISES. 

quires  some  intermediate  statements  before  the  conclusion  may 
be  drawn.  These  intermediate  processes  are  called  premises. 

(g)  Mediate  inference  is  the  total  of  a  series  of  conclusions 
considered  according  to  specifications,  part  of  which  are  con- 
sidered in  the  major  premise  and  part  in  the  minor. 

(//)  Mediate  inference  is  inference  drawn  from  more  than  one 
premise. 

CHAPTERS   XIII— XVI. 

I.  Arrange  the  propositions  in  the  following  syllogisms  so  as 
to  have  the  major  premise  first,  the  minor  premise  second,  and 
the  conclusion  last ;  tell  the  quantity  and  quality  of  eacr.  propo- 
sition ;  tell  also  the  figure  of  each  syllogism,  whether  it  is  valid, 
and  what  caution  it  breaks  if  it  is  not. 

(a)  All  A's  are  B  ;  all  B's  are  C  ;  therefore  all  A's  are  C. 

(b)  No  A  is  C  ;  for  no  A  is  B  and  all  B's  are  C. 

(c)  Some  A's  are  B  and  some  B's  are  C  ;   therefore  some  A's 
are  C. 

(d)  All  A's  are  B  and  some  B's  are  C  ;  therefore  some  A's 
are  C. 

(<?)  No  B  is  A  ;  all  C's  are  B  ;  therefore  some  C  is  not  A. 

(/)  All  B's  are  C  ;  all  A's  are  C  ;  therefore  all  A's  are  B. 

(g~)  This  cannot  be  S's  boy  Jack  ;  for  I  saw  Jack  ten  minutes 
after  he  was  born  and  his  body  was  covered  with  dark  hair, 
and  this  child's  is  not. 

(//)  Every  A  is  C  and  some  B's  are  not  C  ;  therefore  some 
A's  are  not  B. 

(/)  It  is  not  true  that  a  man  cannot  do  a  great  work  without 
a  strong  physique,  for  the  philosopher  Kant  did  a  great  work 
and  his  physique  was  anything  but  strong. 

(j)  B  has  the  kindest  of  feelings  towards  everybody  ;  there- 
fore the  man  you  saw  in  a  violent  altercation  with  his  wife 
could  not  have  been  he. 

(k)  There  must  be  some  invariable  connection  between  red 
hair  and  a  hasty  temper,  for  every  red-haired  person  I  know  is 
quick-tempered. 

(I )  All  B's  are  C  ;  no  A  is  C  ;  therefore  no  A  is  B. 

(in}  A  and  B  each  examined  all  the  specimens  he  could  find( 
and  A  noticed  that  in  every  case  a  certain  feather  in  the  tail 
was  bent  or  broken,  while  B  noticed  that  in  nearly  every  case 


EXERCISES.  463 

there  was  a  scar  near  one  of  the  eyes.     Whatever  the  cause,  it 
is  evident  that  these  two  strange  peculiarities  often  coincide. 

•2a.  What  caution  or  cautions  are  embodied  in  the  following 
proverbs  : 

(1)  All  that  glitters  is  not  gold. 

(2)  One  swallow  doesn't  make  a  summer. 

2/>.  Find  or  make  corresponding  proverbs  for  as  many  of  the 
other  cautions  as  you  can. 

3.  A  is  B  and   B  is  C,  therefore  A  is  C.     Reasoning  on  the 
same  principle,   may  we  not  say  •    Polytheism    is    superstition, 
and  superstition  is  everywhere,  therefore  polytheism  is  every- 
where ? 

4.  What  fault,  if  any,  is  to  he  found  with  the  following  argu- 
ments ?  Show  ho\v  they  can  be  tested  bv  Euler's  diagrams. 

(<i)  Some  men  are  heroes;  J.  S.  is  a  m.,n  ;  therefore  J.  S.  is  a 
hero. 

('•)  All  men  are  heroes;  J.  S.  is  not  a  man  ;  therefore  J.  S.  is 
not  a  hero. 

(c)  All  men  are  heroes;  J.  S.  is  a  hero;  therefore  J.  S.  is  a 
man. 

(if)  lie  must  come  from  B.  ;  for  every  tfne  that  comes  from 
there  has  that  same  way  of  pronouncing  his  r's. 

((•)  Some  men  are  wise,  and  some  men  are  good  ,  therefore 
some  wise  men  are  good. 

(/")  No  man  is  perfect;  this  goat  is  no  man  ;  therefore  this 
goat  is  perfect. 

(.;•)  No  men  are  thoroughly  unselfish;  some  women  are; 
therefore  some  men  at  least  are  not  women. 

(Ji)  All  men  arc  animals  and  no  animals  are  myths  ;  therefore 
no  men  are  myths,  and  Homer  really  lived. 

(/)  Few  towns  ia  the  United  Kingdom  have  more  than 
300,000  inhabitants :  and  as  all  such  towns  ought  to  be  repre- 
sented by  three  members  of  Parliament,  it  is  evident  that  few 
towns  ought  to  have  three  representatives.  (].) 

(/)  Only  animals  are  sentient  beings;  fishes  are  animals; 
therefore  fishes  are  sentient  beings.  (Ray.) 

5.  Give  all  the  conclusions  that  can  be  drawn  from  each  of 
the  following  pairs  of  premises  : 

(u)   Every  A  is  B,  and  no  B  is  C. 

(.'•)  Every  A  is  B,  and  this  C  is  not  A. 

(c)  No  A  is  B,  and  some  C's  are  A. 


464  EXERCISES. 

(//)  No  A  is  B,  but  this  C  is  B. 
(e)  Every  A  is  B,  but  some  C's  are  not  B. 
(/)  Some  B's  are  A  and  some  B's  are  C. 
(g)  Some  B's  are  A,  but  no  B's  are  C. 

6.  Supply  the  missing  premise  in  the  following  syllogisms  : 
(a)  All  A's  are  C  ;  for  all  A's  are  B,  and — 

(/>)  Some  A's  are  not  C  ;  for  some  A's  are  B,  and — 

(c)  None    but    non-A's    are    non-C's ;    for   all    non-B's    are 
non-A's,  and — 

(d)  All  A's  are  non-C's  ;  for  no  A's  are  non-B's,  and — 

(e)  Some  A's  are  not  non-C's  ;  for  no  non-C  is  B,  and — 

7.  Show  that  the  '  rules  of  the  syllogism  '  given  in  the  foot- 
note to  page  177  can  be  inferred  from  the  '  cautions  '  given  in 
preceding  chapters. 

8.  Make  a  set  of  arguments   each  one   of  which    breaks   a 
different  caution,  and  show  how  each  of  them  also  breaks  the 
4  rules  of  the  syllogism  '. 

9.  Is  it  possible  for  both  major  and  minor  terms  to  be  par- 
ticular at  the  same  time  in  the  premises?     If  so,  construct  an 
argument  where  this  is  the  case.     (C.) 

10.  Reduce  the  following  argument  in  the  fourth  figure  to 
each  in  turn  of  the  other  three  : 

Some  B  is  A- 

No  C  is  B  ; 

Therefore  some  A  is  not  C. 


CHAPTER  XVII. 

i.  Criticise  the  following  definitions  : 

(<n)   An  ENTHYMEME  is  an  imperfect  syllogism. 

(a2)  An  enthymeme  is  an  incomplete  syllogism. 

(^3)  An  enthymeme  is  a  syllogism  some  one  or  two  of  whose 
premises  or  conclusion  are  imperfectly  expressed. 

(<?_(.)  An  enthymeme  is  a  misstated  syllogism  ;  that  is,  one  in 
which  one  of  the  premises  is  wanting. 

(b\)  A  DILEMMA  consists  in  assuming  two  assertions,  but 
proves  something  in  cither  case. 

(l>2)  A  dilemma  is  a  disjunctive  proposition  in  which  there 
are  two  alternatives. 


EXERCISES.  465 

(^3)  A  dilemma  is  when  there  is  no  escape  from  two  proposi- 
tions. If  one  is  false,  the  other  must  be  true,  and  vice  versa  ; 
there  can  be  no  half-way  ground. 

(bjf)  A  dilemma  is  a  combination  of  the  disjunctive  and  hy- 
pothetical, such  that  no  true  conclusion  can  be  drawn. 

(c\)  By  SORITES  is  meant  a  syllogism  composed  of  the  three 
propositions  O,  I,  E. 

(c2)  Sorites  contains  a  series  of  syllogisms  imperfectly  ex- 
pressed. 

(r3)  Sorites  is  a  compound  syllogism  and  may  be  decom- 
posed into  single  syllogisms. 

(t/\)  An  EPICHEIREMA  is  a  syllogism  one  of  whose  premises 
proves  or  gives  a  reason  for  another  premise. 

(</2)  An  epicheirema  is  a  syllogistic  statement  so  framed  as 
to  contain  the  conclusion  of  one  part  as  the  prosyllogism  of 
another,  and  so  on. 

(</3)  Epicheirema  is  a  syllogism  furnishing  reason  for  premise 
of  another  syllogism,  or  a  syllogism  one  of  whose  premises  is 
the  conclusion  of  another. 

0/4)  Epicheirema  is  the  name  given  to  the  process  of  proving 
a  statement  by  a  prosyllogism. 

(//5)  An  epicheirema  is  a  statement  which  gives  a  reason  for 
that  statement. 

(d6)  An  epicheirema  is  a  syllogism  that  depends  upon  an  in- 
complete episyllogism. 

(itj)  Epicheirema  is  a  syllogism  in  which  the  propositions  are 
not  all  present. 

(<fS)  Epicheirema  is  a  syllogism  that  gets  its  reason  for  a 
proposition  from  the  syllogism  before  it. 

(<?i)  A  DESTRUCTIVE  DILEMMA  is  a  disjunctive  proposition 
in  which  either  horn  of  the  dilemma  is  not  true. 

(c'2*)  A  destructive  dilemma  is  a  syllogism  in  hypothetical 
form,  only  with  two  different  antecedents  in  the  major  premise 
for  the  same  consequent.  It  is  called  destructive  because  the 
consequent  is  denied. 

(<?3)  A  destructive  dilemma  is  the  one  known  as  the  modus 
ponendo  tollens,  wrhere  by  affirming  the  consequent  is  denied. 

(^4)  A  destructive  dilemma  is  a  syllogism  in  which  the  major 
term  is  a  disjunctive  proposition  and  the  minor  term  is  a  cate- 
gorical proposition  ;  from  which  the  conclusion  is  derived  by 
modus  ponendo  tollens. 


466  EXERCISES. 

(>5)  A  destructive  dilemma  consists  of  two  syllogisms  which 
break  the  validity  of  each  other. 

(e6)  A  destructive  dilemma  is  a  complex  dilemma  and  con- 
sists of  two  alternatives  called  horns,  both  of  which  are  denied 
in  the  course  of  the  argument. 

(<?7)  A  destructive  dilemma  consists  of  a  complex  dilemma, 
that  is,  a  syllogism  in  which  the  major  premise  consists  of  a 
hypothetical  proposition  with  two  or  more  antecedents,  and  a 
minor  premise  consisting  of  disjunctive  proposition. 

2.  Give  two  examples   each    of   a   constructive   hypothetical 
syllogism,  a  destructive    hypothetical   syllogism,  a   disjunctive 
syllogism,  a  simple  constructive  dilemma,  a  complex  construc- 
tive dilemma,  a  destructive  dilemma,  an  epicheirema,  an  enthy- 
meme,  and  a  sorites.     Make  sure  that  each  of  these  is  valid. 

3.  '  If  they  do  not  work,  they  go  hungry.'     Assuming  this  to 
be  true,  what  happens  when  one  of  the  following  statements  is 
also  true  ? — 

(a)  They  do  not  work  ; 
(v)  They  do  not  go  hungry  ; 
(c)  They  work  ; 
(if)  They  go  hungry. 

(4)  Reduce  the  following  arguments  to  a  recognized  form  and 
determine  whether  they  are  valid  or  not: 

(a)  All  D's  are  E,  all  C's  are  D,  all  B's  are  C,  and  no  A's  are 
13  ;  therefore  no  E  is  A. 

(b)  All  J's  are  L,  ail  C's  are  non-V,  all  J's  are  W,  all  L's  are 
C;  and  therefore  some  W's  are  not  Vs. 

(c)  Some  E's  are  A  ;  for  all  non-E's  are  non-D,  no  C's  are 
non-D,  all  B's  are  C,  and  all  non-B's  are  non-A's. 

5.  With  each  of  the  following  tell  the  kind  of  argument.  Is  it 
valid  ?  If  not,  what  caution  is  broken  or  what  fallacy  is  com- 
mitted ?  Reduce  the  argument  to  categorical  form  if  it  is  ca- 
pable of  such  reduction  ;  and  also  if  it  is  hypothetical  reduce  it 
to  disjunctive  form,  and  i'ice  versa.  Show  what  fallacy  the  ar- 
gument commits  in  these  new  forms. 

(a)  If  his  conscience  disapproved  of  the  act,  it  was  certainly 
wrong  for  him  to  do  it,  but  his  conscience  did  not  disapprove, 
therefore  it  was  not  wrong  for  him  to  do  it. 

(l>)  No  honest  man  can  advocate  a  change  in  the  creed  of  his 
church  ;  for  he  must  either  believe  it  or  not  believe  it,  and  if  he 
believes  it  he  cannot  honestly  help  to  change  it,  while  if  lit 


EXERCISES.  467 

does  not  believe  it  he  cannot  honestly  belong  to   the   church 
at  all. 

(c)  Protection  from  punishment  is  plainly  due  to  the  inno- 
cent;  therefore,  as  you  maintain  that  this  person  ought  not  to 
be  punished,  it  appears  that  you  are  convinced  of  his  innocence. 
(W.) 

(d)  If  men  are  not  likely  to  be  influenced  in  the  performance 
of  a  known  duty  by  taking  an  oath  to  perform  it,  the  oaths  com- 
monly administered  are  superfluous  ;  if  they  are  likely  to  be  so 
influenced,  every  one  should  be  made  to  take  an  oath  to  behave 
rightly  throughout  his  life.     But  one  or  other  of  these  must 
be  the  case  ;  therefore  either  the  oaths  commonly  administered 
are  superfluous,  or  every  man  should  be  made  to  take  an  oath 
to  behave  rightly  throughout  his  life.     (W.) 

(V)  The  child  of  Themistocles  governed  his  mother  ;  she  gov- 
erned her  husband  ;  he  governed  Athens  ;  Athens,  Greece  ;  and 
Greece,  the  world  :  therefore  the  child  of  Themistocles  gov- 
erned the  world.  (W.) 

(/)  It  is  worth  while  to  teach  the  elements  of  Latin  in  the 
public  schools  if  this  gives  the  minds  of  the  pupils  a  good  gen- 
eral training,  or  if  it  gives  most  of  the  pupils  a  useful  insight 
into  Roman  life  and  literature,  or  if  most  of  them  will  continue 
the  study  in  a  college  course.  But  none  of  these  alternatives 
is  true  ;  therefore  it  is  not  worth  while  to  teach  the  elements 
of  Latin  in  the  public  schools. 

(g)  If  every  ghost  story  is  to  be  believed,  we  must  accept 
the  general  standpoint  of  the  'spiritualists';  but  we  cannot 
accept  their  general  standpoint;  therefore  we  cannot  believe 
ghost  stories. 

(//)  If  transportation  is  not  felt  as  a  severe  punishment,  it  is 
in  itself  ill  suited  to  the  prevention  of  crime;  if  it  is  so  felt, 
much  of  its  severity  is  wasted,  from  its  taking  place  at  too  great 
a  distance  to  affect  the  feelings,  or  even  come  to  the  knowledge, 
of  most  of  those  whom  it  is  designed  to  deter;  but  one  or 
other  of  these  must  be  the  case  :  therefore  transportation  is 
not  calculated  to  answer  the  purpose  of  preventing  crime.  (W.) 

(z')  If  virtue  is  voluntary,  vice  is  voluntary  ;  virtue  is  volun- 
tary ;  therefore  so  is  vice.  (Aristotle.) 


EXERCISES. 


CHAPTER  XVIII. 

Criticise  the  following  definitions  : 

(ai)  A  FALLACY  is  a  statement  which  is  not  true. 

(<72)  When  wrong  meaning  is  given  to  a  statement  it  is  called 
a  fallacy. 

(«3)   Fallacy  is  a  mistake  in  term. 

(«4)  A  fallacy  is  a  false  conclusion  drawn  from  two  premises. 

(#5)  A  fallacy  is  the  incorrect  use  of  the  laws  governing 
thought. 

(a6)  A  fallacy  is  an  untruth — a  flaw.  If  you  detect  a  flaw  in 
a  proposition,  you  have  found  a  fallacy  in  the  proposition. 

(aj)  If  a  method  of  reasoning  is  so  used  as  to  make  state- 
ments or  conclusions  contradictory,  a  fallacy  is  made. 

(a8)  A  fallacy  is  a  syllogism  in  which  an  incorrect  conclusion 
is  drawn. 

(ag)  A  faHacy  is  a  false  judgment. 

(/'i)  A  MATERIAL  FALLACY  is  a  fallacy  which  arises  from  the 
use  of  more  than  three  terms,  more  than  three  propositions,  or 
ambiguous  words,  or  an  improperly  stated  syllogism. 

(b2)  A  material  fallacy  is  a  fallacy  in  the  word  or  words  of  a 
proposition. 

(<$3)  A  material  fallacy  is  one  in  which  there  is  a  breach  in  the 
subject-matter. 

CHAPTER  XIX. 

1.  Criticise  the  following  definitions  : 

(a\)  PETITIO  PRIXCIPII  is  the  fallacy  of  begging  the  question. 

(a2)  The  fallacy  of  petitio  principii  is  using  one  of  the  prem- 
ises in  the  conclusion. 

(b2)  IGNORATIO  F.LENCHI  is  a  fallacy  of  imperfect  reasoning  ; 
that  is,  what  follows  is  not  true. 

(l>2)  Ignoratio  elenchi  is  a  fallacy  in  which  the  premises  and 
conclusion  have  no  distinct  connection. 

(^3)  Ignoratio  elenchi  is  the  fallacy  committed  when  a  con- 
clusion is  drawn  which  may  have  some  bearing  upon  what  has 
been  said  in  the  premises,  but  which  does  not  logically  follow. 

2.  Consider  whether  the  assumption  of  a  false  premise  may 
be  fairly  regarded  as  a  case  of  begging  the  question. 


EXERCISES.  469 

3.  Make  or  find  two  examples  besides  those  given  in  the  text 
of  each  of  the  fallacies  there  explained. 

4.  Criticise  the  following  arguments  or  implied  arguments  : 
(a)  Written  examinations  are  not  an  absolutely  fair  test  of  a 

student's   scholarship — much    less  of  his    industry  and  intelli- 
gence.    It  is  therefore  wrong  to  base  his  grade  upon  them. 

(6)  Municipal  ownership  of  street-cars  would  be  beneficial  to 
the  people,  and  what  is  beneficial  to  the  people  should  be  put 
into  practice  ;  therefore  the  street-cars  under  private  ownership 
should  not  be  patronized. 

(c)  It  is  wrong  to  take  the  life  of  a  fellow  man,  for  God  has 
distinctly  commanded  us  not  to,  and  it  is  wicked  to  disobey 
his  commandments.     If  any  one  pretends  to  doubt   that  this 
commandment  really  did  come  from  God,  I  can  only  appeal  to 
his  own  conscience  and   his  own  common  sense.    When  God 
gave   the    commandments   to  his  people    is  it   likely  that   he 
would  have  omitted  the  most  important  of  them  all — a  com- 
mandment which  only  expresses   the   natural  feeling  of  every 
normal  human  being? 

(d)  "  America  has  still  a  long  vista  of  years  stretching  before 
her  in  which  she  will  enjoy  conditions  far  more  auspicious  than 
any    European    country   can   count  upon.     And  that  America 
marks  the  highest  level,  not  only  of  material  well-being,  but  of 
intelligence   and  happiness,  which  the  race   has  yet   attained, 
will  be  the  judgment  of  those  who  look  not  at  the  favored  few 
for  whose  benefit  the  world  seems  hitherto  to  have  framed  its 
institutions,  but   at   the  whole    body  of  the  people."     (James 
Bryce.) 

(e)  "  It  no  doubt  wounds  the  vanity  of  a  philosopher  who  is 
just  ready  with  a  new  solution  of  the  universe  to  be  told  to 
mind  his  own  business  [laissez  faire].     So  he  goes  on  to  tell  us 
that  if  we  think  that  we  shall,  by  being  let  alone,  attain  to  per- 
fect happiness  on  earth,  we  are  mistaken.     The  half-way  men — 
the    professorial    socialists — join    him.      They   solemnly   shake 
their  heads,  and  tell  us  that  he  is  right — that  letting  us  alone 
will    never   secure   us   perfect   happiness."      (W.    G.  Sumner.) 
What  fallacy  do  they  commit  ? 

(/")  'Every  particle  of  matter  gravitates  equally.'  'Why?' 
'  Because  those  bodies  which  contain  more  particles  ever  gravi- 
tate more  strongly,  i.e.,  are  heavier.'  '  But',  it  may  be  urged, 
'  those  which  are  heaviest  are  not  always  more  bulky  '.  '  No,  but 


47°  EXERCISES. 

still  they  contain  more  particles,  though  more  closely  con- 
densed.' 'How  do  you  know  that?'  'Because  they  are 
heavier.'  '  How  does  that  prove  it  ?  '  '  Because,  all  particles  of 
matter  gravitating  equally,  that  mass  which  is  specifically  the 
heavier  must  needs  have  the  more  of  them  in  the  same  space.' 
(W.) 

(g)  Those  are  your  arguments  against  the  course  of  conduct 
I  propose  ;  and  yet  the  fact  remains  that  when  you  were  in  my 
position  you  did  the  very  thing  that  you  are  now  advising  me 
not  to  do. 

(//)  Everybody  ought  to  contribute  something  to  the  support 
of  the  unfortunate  ;  therefore  there  is  no  harm  in  a  law  which 
compels  him  to  do  so. 

(/)  "  Again,  we  are  not  inclined  to  ascribe  much  practical 
value  to  that  analysis  of  the  inductive  method  which  Bacon 
has  given  in  the  second  book  of  the  Novum  Organum.  It  is, 
indeed,  an  elaborate  and  correct  analysis.  But  it  is  an  analysis  of 
that  which  we  are  all  doing  from  morning  to  night,  and  which 
we  continue  to  do  even  in  our  dreams."  (Macaulay.) 

5.  Examine  the  arguments  or  implied  arguments  in  the  follow- 
ing passages  from  Trumbull's  "  Lie  never  justifiable  ".  The 
first  of  them  may  be  regarded  as  an  introduction  to  the  history 
of  the  discussion. 

(a)  "  Because  of  the  obvious  gain  in  lying  in  times  of  extrem- 
ity, and  because  of  the  manifest  peril  or  cost  of  truth-telling  in 
an  emergency,  attempts  have  been  made,  by  interested  or  prej- 
udiced persons,  all  along  the  ages,  to  reconcile  the  general  duty 
of  adhering  to  an  absolute  standard  of  right,  with  the  special 
inducements,  or  temptations,  to  depart  from  that  standard  for 
the  time  being."  (p.  81.) 

(l>)  "  All  the  refinements  of  casuistry  have  their  value  to  those 
who  admit  that  a  lie  may  be  right  under  certain  conceivable 
circumstances  ;  but  to  those  who,  like  Augustine  and  Aquinas, 
insist  that  a  lie  is  a  sin  per  se,  and  therefore  never  admissible, 
casuistry  itself  has  no  interest  as  a  means  of  showing  when  a  sin 
is  not  sinful."  (p.  1 14.) 

(c)  "  When    he    attempts   the    definition    of  a   lie,    however, 
Jeremy  Taylor  would  seem  to  claim  that  injustice  to  others  and 
an  evil   motive   are   of  its  very  essence,  and  that,  if  these  be 
lacking,  a  lie  is  not  a  lie."     (p.  1 17.) 

(d)  "  As  to  falsifying  to  a  sick  or  dying  man,  he  [Dorner] 


EXERCISES.  471 

says  'we  overestimate  the  value  of  human  life,  and,  besides,  in 
a  measure  usurp  the  place  of  Providence,  when  we  believe  we 
may  save  it  by  committing  sin.'  "  (p.  132.) 

(e)  "A  lie  being  a  sin  far  se,  no  price  paid  for  it  ...  would 
make  it  other  than  a  sin.  ...  It  was  a  heathen  maxim,  '  Do 
right  though  the  heavens  fall, 'and  Christian  ethics  ought  not 
to  have  a  lower  standard  than  that  of  the  best  heathen  morality." 
(pp.  78,  79.) 

(f)  "  God  cannot  justify  or  approve  a  lie.     Hence  it  follows 
that  he  who  deliberately  lies  in  order  to  secure  a  gain  to  him- 
self, or  to  one  whom  he  loves,  must  by  that  very  act  leave  the 
service  of  God,  and  put  himself  for  the  time  being  under  the 
rule  of  the  '  father  of  lies  '."     (p.  79.) 

(_£•)  "It  is  a  physician's  duty  to  conceal  from  a  patient  his 
sense  of  the  grave  dangers  disclosed  to  his  professional  eye,  and 
which  he  is  endeavoring  to  meet  successfully.  And  in  well- 
nigh  every  case  it  is  possible  for  him  to  give  truthful  answers 
that  will  conceal  from  the  patient  what  he  ought  to  conceal  ; 
for  the  best  physicians  do  not  know  the  future,  and  his  profes- 
sional guesses  are  not  to  be  put  forward  as  if  they  were  assured 
certitudes."  (p.  75.) 

CHAPTER   XX. 

1.  Criticise  the  following  definitions  : 

(a)  A    fallacy  of   MANY  QUESTIONS   is  one    in   which    many 
irrelevant  questions  are  asked  which  cannot  be  answered   di- 
rectly by  Yes  or  No  and  which  confuse  the  argument. 

(b)  The  fallacy  of  many   questions  is  the  use  of  more  data 
than  are  needed  to  prove  the  premises. 

(c)  A  fallacy  of  many  questions  is  the  result  of  a  false  suppo- 
sition. 

((/)  The  fallacy  of  many  questions  consists  in  asking  two  or 
more  questions  at  the  same  time  so  that  it  is  impossible  to  give 
a  correct  answer. 

((?)  The  fallacy  of  many  questions  is  using  so  many  questions 
in  the  argument  that  the  conclusion  does  not  stand  out  clearly. 

(_/)  The  fallacy  of  many  questions  consists  in  asking  two  or 
more  questions  in  one. 

2.  What  fallacies,  if  any,  are  committed  or  exposed  in  the 
following  : 


47 2  EXERCISES- 

(a)  'We  were  put  in  this  world  to  help  others.'     '  And  what 
are  others  here  for  ?  ' 

(b)  "  If  any  one  thinks  that  there  are  or  ought  to  be  in  society 
guarantees  that  no  man  shall  suffer  hardship,  let  him  under- 
stand that  there  can  be  no  such  guarantees,  unless  some  other 
men  give  them."     (W.  G.  Sumner,  op.  cit.) 

(c)  Old  age  is  wiser  than  youth.     We  should  therefore  pay 
great  deference  to  the  convictions  of  the  ancients. 

(d)  'There  never  was  an  Irishman  so  poor  that  he  did   not 
have  a  still  poorer  Irishman  living  at  his  expense.' 

(e)  '  Habit  is  the  cable  which  has  grown    so  strong  by  use 
that  its  victim  cannot  depart  from  it.' 

(/)  Thought  is  nothing  but  a  movement  of  the  brain. 

(g)  "There  is  a  beautiful  notion  afloat  in  our  literature  and 
in  the  minds  of  our  people  that  men  are  born  to  certain  '  natu- 
ral rights.'  ...  If  there  were  such  things  as  natural  rights,  the 
question  would  arise,  Against  whom  are  they  good  ?  Who 
has  the  corresponding  obligation  to  satisfy  these  rights? 
There  can  be  no  rights  against  Nature,  except  to  get  out  of  her 
whatever  we  can,  which  is  only  the  fact  of  the  struggle  for 
existence  stated  over  again.  The  common  assertion  is  that  the 
rights  are  good  against  society  ;  that  is,  that  society  is  bound 
to  obtain  and  secure  them  for  the  persons  interested.  Society, 
however,  is  only  the  persons  interested  plus  some  other  persons  ; 
and  as  the  persons  interested  have  by  the  hypothesis  failed  to 
win  the  rights,  we  come  to  this,  that  natural  rights  are  the 
claims  which  certain  persons  have  by  prerogative  against  some 
other  persons.  Such  is  the  actual  interpertation  in  practice  of 
natural  rights — claims  which  some  people  have  by  prerogative 
on  other  people."  (W.  G.  Sumner,  op.  cit.) 

(A)  And  if  a  spark  has  been  kindled  by  the  exercises  of  this 
day,  let  us  water  that  spark. 

(/)  The  sultan  dreamed  that  all  his  teeth  had  fallen  out,  and 
summoned  the  soothsayers  to  tell  him  what  it  meant : 

"  At  last  an  old  soothsayer,  wrinkled  and  gray, 
Cried,  '  Pardon,  my  lord,  what  I  have  to  say  ; 

'Tis  an  omen  of  sorrow  sent  from  on  high  ; 
Thou  shalt  see  all  thy  kindred  die.' 

Wroth  was  the  sultan  ;  he  gnashed  his  teeth, 
And  his  very  words  seemed  to  hiss  and  seethe, 


EXERCISES.  473 

And  he  ordered  the  wise  man  bound  with  chains, 
And  gave  him  a  hundred  stripes  for  his  pains. 

The  wise  men  shook  as  the  sultan's  eye 
Swept  round  to  see  who  next  would  try  ; 

But  one  of  them,  stepping  before  the  throne, 
Exclaimed  in  a  loud  and  joyous  tone  : 

'  Exult,  O  head  of  a  happy  state  ! 
Rejoice,  O  heir  of  a  happy  fate  ! 

For  this  is  the  favor  thou  shalt  win, 
O  Sultan,  to  outlive  all  thy  kin.' 

Pleased  was  the  sultan  and  called  a  slave, 
And  a  hundred  crowns  to  the  wise  man  gave." 

(f)  The  claimant  has  undoubtedly  many  peculiarities  of  gait 
and  manner  which  were  characteristic  of  the  missing  baronet. 
Are  not  these  therefore  proofs  of  identity  equivalent  to  the 
evidence  of  imposture  afforded  by  the  absence  of  tattoo-marks 
which  the  genuine  man  is  proved  to  have  possessed  ?  (J.) 

(k)  Human  powers  are  bounded  only  by  the  infinite.  (D. 
altd.) 

(/)   Hoc  unum  scio,  quod  nihil  scio. 

(m)  God  separated  the  different  races  of  men  ;  then  why 
should  we  encourage  immigration  that  will  mix  them  up  again  ? 

(11)  "  A  lie  is  inconsistent  with  confidence  ;  and  the  knowl- 
edge that  a  lie  is,  under  certain  circumstances,  deemed  proper 
by  a  man,  throws  doubt  on  all  that  the  man  says  or  does  under 
any  circumstances.  No  matter  why  or  where  the  one  opening 
for  an  allowable  he  be  made  in  the  reservoir  of  public  confi- 
dence, if  it  be  made  at  all,  the  final  emptying  of  that  reservoir 
is  merely  a  question  of  time."  (Trumbull,  p.  227.) 

(o)  According  to  Professor  Sumner  "  the  possession  of  capi- 
tal is  an  indispensable  prerequisite  of  educational,  scientific, 
and  moral  goods  ".  Now  a  man  who  possesses  no  moral  goods 
is  not  a  good  man,  and  a  man  without  educational  goods  is  not 
educated.  From  all  of  which  it  follows  that  according  to  Pro- 
fessor Sumner  the  capitalists  are  the  only  people  in  the  com- 
munity who  are  either  good  or  educated. 

(P)  A  man  who  has  money  enough  to  obtain  the  be?t  food, 
the  best  tools,  and  the  best  care  when  he  is  sick  has  a  great 


474  EXERCISES. 

advantage  over  his  rivals  in  the  struggle  for  existence.  But 
what  is  to  the  advantage  of  one  man  in  this  struggle  is  to  the 
disadvantage  of  his  competitors;  and  thus  it  happens  that  by 
the  very  fact  of  bringing  life  to  the  rich  man  the  money  which 
he  possesses  often  brings  death  to  his  poorer  rival. 

(y)  All  the  great  financial  crimes  that  we  read  about  are 
committed  by  bankers  and  stock-brokers.  Therefore  the  coun- 
try would  be  a  great  deal  better  off  if  banks  and  stock  ex- 
changes were  abolished. 

(r)  '  They  tell  us  that  \ve  are  weak,  unable  to  cope  with  so 
formidable  an  adversary;  but  when  shall  we  be  stronger  ?  ' 
(s)  "  When  I  have  grown  to  man's  estate 

I  shall  be  very  proud  and  great, 
And  tell  the  other  girls  and  boys 
Not  to  meddle  with  my  toys." 

(R.  L.  Stevenson.) 

(/)  Whatever  is  universally  believed  must  be  true ;  the  exist- 
ence of  God  is  not  universally  believed;  therefore  it  is  not 
true.  (W.) 

CHAPTERS  XXI— XXV. 

1.  "A,  B,  C,  D,  and  E  are  the  only  German  students  I  know; 
they  are  all  men  of  considerable  intellectual  attainments,  and 
consequently  I  may  infer  that  all  German  students  are  men  of 
considerable  intellectual  attainments."     (F.)     Is  this  argument 
inductive  or  deductive?     Is  it  valid?     If  so,  how  much  confi- 
dence can  be  attached  to  the  conclusion  ? 

2.  Why  are  we  able  to  reach  many  conclusions  by  induction 
that  cannot  be  reached  by  deduction  ? 

3.  '  I  have  no  confidence  in  a  Chinaman,  for  the  Chinese  gov- 
ernment is  one  of  the  most  corrupt  in  the  world.'     Estimate 
the  value  of  such  an  inference. 

4.  Should  we  seek  for  the  causes  of  things,  or  merely  of  their 
states   and    relations?     Is  there  any  objection  to  speaking  of 
a    thing   as    '  cause   of   itself  '  ?      (See   definition    in    Spinoza's 
"Ethic".) 

5.  What  fallacy  is  committed  by  a  man  who  passes  counter- 
feit money  on  the  ground  that  the  public  has  given  it  to  him 
and  the  public  ought  to  get  it  back  again  ? 

6.  Is   there  any  objection   to  the    following   explanation  ?— 


EXERCISES.  475 

1  People  get  tired  because  everything  they  do  involves  some 
action  on  the  part  of  the  cells  in  their  brain.  These  cells,  like 
all  other  cells,  are  probably  living  creatures,  and  as  such  they 
are  subject  to  the  universal  law  of  fatigue.' 

7.  "  The  analysis  of  a  fact  consists  in  the  process  of  distin- 
guishing mentally  between  its  different  details  (the  various 
episodes  of  an  event,  the  characteristics  of  an  institution),  with 
the  object  of  paying  special  attention  to  each  detail  in  turn; 
that  is  what  is  called  examining  the  different  'aspects'  of  a 
fact, — another  metaphor."  (Langlois-Seignobos.)  In  the  light 
of  this,  consider  the  possibility  of  modifying  statements  in 
Chapter  XXII  in  which  the  word  '  aspect '  is  used. 

£.  Give  some  examples  of  explaining  in  a  circle — '  circulus  in 
explicando.' 

9.  Give  some  examples  of  a  '  Perfect  Induction  '  and  of  an 
Inductio  per  Enumerationem  Simplicem. 

10.  Give  some  examples  of  your  own  to  show  how  we  assume 
relations  of  identity  and  general  laws  in  discovering  relations  of 
causation,  and  similarly  with  each  of  the  other  two. 

11.  How  would  you  prove  that  the  rotation  of  the  earth  is 
not  due  in  large  measure  to  the  constant  influence  of  the  fixed 
stars  ?      How  would  you  prove,  on  the  other  hand,  that  the 
rotation  is  not  due  to  the  influence  of  some  demon  inhabiting  it  ? 

12.  Give  examples  of  your  own- showing  how  causal  analy- 
sis gives  definiteness  of  conception  and   greater  reliability  of 
inference. 


CHAPTERS  XXVI— XXXI. 

1.  With   the    following    combinations    of   antecedents    and 
consequents,  find   the   cause    of  L.     What    is  the   method  ? — 
ACDEKLMN,  ACEKMN. 

2.  What  causal  relation  is  suggested  by  the  following  com- 
binations ?     Is  it  suggested  only,  or  proved   to  exist?     What 
is    the    method?— ABCFNOPQ,    CDEGLMNT,   CHIJNRS, 
BCENOT. 

3.  Find  a  set  of  causal  relations  that  will  account  for  the  fol- 
lowing combinations.     What  is  the  method? — ABCDNOPO, 
BCDOPQ,  EFRS,  ABENR,  AFDPQS,  BEGRTU. 

4.  Do   the   same   with   this:   ABCDUNQ,    ABEFUNOPR, 
CDEFQTOPR,  BEGNOS. 


476 


EXERCISES. 


5.  Do  the  same  with  this  :  ABCDZ,  ACEPQRX,  BCEQXZ, 
ACFPRVX,  DEFQV,  ADFPV. 

6.  Do  the  same  with   this:   ABCPQST,  ACDPSTO, 
CDESTOV,  BDEPQOV,  ADEPSOV,  ACEPSTV. 

7.  Do  the  same  with  this  :  ABCPST,  ABDPQS,  ABEPS, 
ABFOPRS,    ACEST,    ACFORST,    ADEQS,     ADFOQRS, 
BCDPQT,   BCEPRT,   BCFOPRT,   BDEPQR,   BDFPQRO, 
CDEQRT,  CDFQT,  CEFORT,  DEFOQR. 

8.  Do    the    same    with    this :    ABCPR,    ABDO,    ABEP, 
ACDOPZ,     ACEPZ,    ADEOPZ,     BCDOPRX,     BCEPRX, 
BDEOPX,     CDEOP,     ABCDOPR,    ABCEPR,    ABDEOP, 
ACDEOPZ,  BCDEOPRX. 

9.  What  inference  can  be  drawn  from  the  following  diagram  ? 

The  distance  of  any  dot  above  the 
line  OB  represents  the  proficiency 
of  some  one  student  in  one  kind  of 
work,  A;  the  distance  from  the  line 
OA  represents  the  proficiency  of 
the  same  student  in  another  kind 
of  work,  B. 

10.  What  inference  could  have 
been  drawn  from  the  diagram  if  the 
dots  had  been  found  to  group  them- 
selves about  a  diagonal  running 
from  A  to  B  ?  If  they  had  been 
line  ?  If  they  had  been  scattered 


0 


B 


grouped  about  a  horizontal 
irregularly  over  the  whole  square? 

11.  What   is   the  significance  of  the  italicized  words  in  the 
following  sentences  ? —  When  he  came  I  left ;  He  arrived  and 
then  there  was  trouble  ;  The  rain  followed  the  lightning. 

12.  Examine  the  reasoning  expressed  in  the  following  : 

(a)  "  Depend   upon  it,  the   best  antiseptic  for  decay  is  an 
active    interest  in   human  affairs:  those  live  longest  who  live 
most." 

(b)  When  this  pond  was  first  fished  in  the  fish  were  very 
numerous  and  very  easily  caught ;  but  now  so  many  of  them 
have  been  caught  that  the  rest  have  grown  very  wary. 

(c)  Children  are  a  good  deal  like  apples — the  first  to  ripen  are 
usually  the  first  to  decay  ;  and  therefore  a  wise  teacher  will  do 
what  he  can  to  delay  the  development  of  those  that  seem  most 
precocious. 


EXERCISES.  477 

(</)  We  all  drank  the  water  and  none  of  us  got  sick  ;  so  this 
outcry  about  the  danger  of  typhoid  is  all  nonsense. 

(e)  Any  one  who  examines  the  records  will  soon  find  out  for 
himself  that  those  students  who  '  scatter  '  most  in  their  choice 
of  studies  are  those  who  accomplish  least  in  any  of  them  ;  and 
when  he  sees  this  he  ought  to  realize  the  harm  that  can  be 
done  by  a  system  of  absolutely  free  electives. 

(/)  Trains  run  with  Blank's  oil  have  made  the  fastest  time 
known  amongst  railway  men. 

(^)          "  A  letter  forged  !  Saint  Jude  to  speed  ! 
Did  ever  knight  so  foul  a  deed  !  .  .  . 
Thanks  to  Saint  Bothan,  son  of  mine, 
Save  Gawain,  ne'er  could  pen  a  line."        (Scott.) 

(K)  'The  rain-maker  is  going  to  fire  off  his  gunpowder  to- 
morrow, but  he  can't  fool  us ;  we  have  a  written  contract  that 
if  there  is  no  rain  there  is  to  be  no  pay/  Examine  the  same 
kind  of  reasoning  with  reference  to  patent  medicines  and  'tips  ' 
on  investments  :  '  no  cure  no  pay  ' — '  no  profits  no  pay.' 

13.  Give  two  examples  of  your  own  of  each  of  the  inductive 
methods  explained  in  these  chapters. 

14.  Give  some  examples  of '  combined '  and  of '  compounded  ' 
causes. 

15.  With  A  as  engineer  and  M  as  fireman  a  certain  locomo- 
tive can  average  sixty-eight  miles  an  hour  ;  with  A  as  engineer 
and  N  as  fireman  it  averages  sixty-three  miles ;  with  B  as  en- 
gineer and   M   as  fireman   it  averages   sixty ;   and  with  B  as 
engineer  and  N  as  fireman  it  averages  fifty-five.     What  part  of 
the  speed  in  each  case  would  you  credit  to  the  locomotive,  and 
what  to  each  of  the  men  ? 

1 6.  The  weight  of  boys  and  girls  of  different  ages   in   the 
public  schools  of  the  United  States  is  about  as  follows :  Boys 
of    six,  43^  Ibs. ;  of  seven,  47^ ;  of  eight,  52^- ;  of  nine,  57^ ;  of 
ten,  62^ ;  of  eleven,  6S£  ;   of  twelve,  73$  ;    of  thirteen,  80 ;  of 
fourteen,  88  ;  of  fifteen,  100;  of  sixteen,  114.     Girls  of  six,  42; 
of  seven,  46  ;  of  eight,  50^  ;   of  nine,  55  ;  of  ten,  604 ;  of  eleven, 
65!  ;  of  twelve,  73  ;  of  thirteen,  83?  ;  of  fourteen,  94;  of  fifteen, 
103;  of  sixteen,  110;  of  seventeen,  115$.     From  these  data  it 
is   usually  inferred  that  girls  have   a  period  of  rapid  growth 
between  the  ages  of  twelve  and  fourteen  or  fifteen,  and  that 


EXERCISES. 

boys  have  a  similar  period  a  couple  of  years  later.     Is  there  any 
other  way  of  accounting  for  the  figures  ? 

17.  "More  men  than  women  die  every  year.  This  is  due  to 
the  greater  mortality  attending  the  life  of  the  male  "  (Mayo- 
Smith,  "  Statistics  and  Sociology  ").  What  does  this  mean  ? 
How  can  it  be  possible?  '  In  Germany  109  men  die  each  year 
for  every  100  women.'  What  can  we  conclude  from  this  ? 
Why  is  it  better  to  know  that  in  Germany  28.6  out  of  every 
thousand  males  die  each  year  and  25.3  out  of  every  thousand 
females?  Since  everybody  must  die  sooner  or  later  how  is  it 
possible  that  there  should  be  in  any  country  (or  in  the  whole 
world)  a  permanently  greater  death-rate  for  one  sex  than  for 
the  other  ? 

CHAPTERS  XXXI— XXXII. 

1.  In  many  gymnasiums  a  prize  is  given  for  'symmetrical  de- 
velopment'.    How  should  this  be  estimated?     Is   there  any 
objection  to  giving  the  prize  to  the  candidate  whose  propor- 
tions approach  nearest  to  the  average  of  all  students  measured  ? 

2.  In  a  study  of  great  men  it  is  found  that  for  thirty-nine 
fathers  and  twenty-five  mothers  the  average  age  of  the  parents 
at  the  time  of  the  birth  of  the  great  man  is  37.78  years  for  the 
former  and  29.8  years  for  the  latter.     "  Although  there  are  few 
cases,  the  results  are  interesting,  because  they  are  in  agreement 
with  those  of  Galton,  who  finds  the  average  age  of  the  parents 
of  one  hundred  English  men  of  science  to  be  thirty-six  years  for 
the  fathers  and  thirty  years  for  the  mothers.  .  .  .  Both  studies 
would  seem  to  show  that  the  child  born  of  parents  in  the  prime 
of  physical  life  has  the  better  chance  of  greatness.     Both  results 
conflict   with  Lombroso's  theory,  which  he  took  from  Mosso, 
that  '  the  number  of  men  of  genius  and  even  of  talent  issued 
from   aged   fathers   is   very  great.' "     (A.    H.    Yoder   in    Ped. 
Sem.  Ill,  137.)    Can  any  fault  be  found  with  these  conclusions  ? 

3.  A  got  a  certain  story  from  B,  B  from  C,  C  from  D,  and  D 
from  E.     In  each  case  there  was  an  even  chance  that  the  hearer 
'  got   it  wrong '.     What  are  the  chances  that  A  got  E's  story 
exactly  as  he  told  it  ? 

4.  Is  there  any  difference  between  saying  that  a  certain  horse 
is  the  most  likely  to  win  the  race  and  saying  that  it  is  likely  to 
win  ? 


EXERCISES.  479 

5.  "  What  an  author  expresses  is  not  always  what  he  believed, 
for  he  may  have  lied  ;  what  he  believed  is  not  necessarily  what 
happened,  for  he  may  have  been  mistaken.     These  propositions 
are  obvious.     And  yet  a  first  and  natural  impulse  leads  us  to 
accept  as  true  every  statement  contained  in  a  document,  which 
is  equivalent  to  assuming  that  no  author  ever  lied  or  was  de- 
ceived."    (Langlois-Seignobos.)     Is  there  any  objection  to  this 
statement  ? 

6.  Account  for  the  saying  that  lightning  never  strikes  twice 
in  the  same  place. 

7.  Is   there  any  objection  to  this  reasoning? — '  The  event  in 
question  must  have  been  either  A,  B,  C,  or  D.     Of  these  A  is 
the  most  probable.     Therefore  the  event  in  question  was  prob- 
ably A.' 

8.  Scarlet  fever  is  one  of  the  most  contagious  of  diseases, 
and  yet  an  eminent  authority  says  he  '  can  find  no   instance 
recorded  where  it  has  been  transmitted  through  two  healthy 
persons '.     If  we  assume  that  such  cases  do  not  exist,  what  can 
we   infer  about  the  number  of  germs  usually  present  in  the 
vicinity  of  a  patient  and  about  the  number  necessary  to  trans- 
mit the  disease  ? 

9.  What  reply  can  be  made  to  the  following  ? — '  You  say  that 
the   prisoner   is   probably  guilty.     I   grant   it.     But  this  only 
means  that  the  prisoners  in  most  cases  of  this  sort  are  guilty. 
It  does  not  mean  that  this  particular  prisoner  has  even  a  touch 
of  guilt.     Your  very  use  of  the  word  '  probable  '  is  a  confession 
that  for  all  you  know  he  may  be   absolutely  innocent.     How 
then  can  you  ask  the  jury  to  condemn  him  to  an  awful  fate  ?  ' 

10.  What  reply  can  be  made  to  the  spiritualist  who  demands 
assent  to  his  explanation  of  certain  phenomena  on  the  ground 
that  it  is  the  most  probable  of  all  the  many  explanations  which 
have   been    offered  ?      Can   we   deny   his   conclusion    without 
denying  the  premises  ? 

11.  Assuming  that  the  difference  between   several  different 
measurements  of  the  same  quantity  is  due  to  a  large  number  of 
different  variables,  each  one  of  which  affects  each  of  the  meas- 
urements to  a   slight  degree,  prove   that  the  mean  of  all  the 
measurements  is  far  more  likely  to  be  nearly  correct  than  either 
of  the  extremes. 


480  EXERCISES. 


CHAPTERS  XXXIII— XXXVI. 

1.  How  much  inference  is  there  in  the  following  '  observa- 
tions '  ? — 

(a)  A  player  catching  a  baseball  at  the  far  side  of  the  field  ; 

(b)  The  observer  himself  shooting  a  bird  ; 

(r)  The  effect  of  a  certain  speech  upon  the  hearer. 

2.  Give    some   instances   in  which   you   yourself  have  '  ob- 
served '  or  '  remembered  '  an  event  that  did  not  take  place. 

3.  Can  you  recall  any  cases  in  which  you  have  made  records 
for  your  own  use  and  then  been  unable  to  find  them  or  to  inter- 
pret them  ?     If  so,  what  was  wrong? 

4.  Recall  any  cases  you  may  know  about  in  which  circum- 
stantial evidence  seemed  convincing,  though  the  conclusion  to 
which  it  pointed  was  afterwards  found  to  be  wrong. 

5.  "  Violenta  presumptio  is  many  times  plena  probatio  ;  as  if 
one  be  run  thorow  the  bodie  with  a  sword  in  a  house,  whereof 
he  instantly  dieth,  and  a  man  is  seen  to  come  out  of  that  house 
with  a  bloody  sword,  and  no  other  man  was  at  that  time  in  the 
house."     (Lord  Coke.)     Explain  exactly  what  this  means,  and 
then  see  how  many  alternative  explanations  you   can  find  for 
the  occurrence  mentioned  in  illustration. 

6.  Estimate  the  value  of  the  following  arguments  : 

(a)  There  must  be  something  in  oracles  ;  for  Herodotus  tells 
many  tales  that  show  the  wonderful  powers  of  the  oracle  at 
Delphi,  and  Herodotus  was  a  careful  and  critical  historian. 

(b}  It  is  fair  to  assume  that  he  was  guilty  of  at  least  some 
misconduct,  for  where  there  is  smoke  there  is  fire,  and  he  has 
certainly  succeeded  in  getting  himself  criticised  by  everybody. 

(c)  The  doctrine  of  the  divine  right  of  kings  was  certainly 
current  in  the  time  of  Elizabeth ;  for  we  read  in  Shakspere : 

"  Not  all  the  water  in  the  rough  rude  sea 
Can  wash  the  balm  off  from  an  anointed  king." 

(«f)  "  To  thine  own  self  be  true, 

And  it  must  follow,  as  the  night  the  day, 
Thou  canst  not  then  be  false  to  any  man." 

These  are  the  words  of  Shakspere,  perhaps  the  greatest  ob- 
server of  human  life  that  ever  existed  ;  and  we  should  value 
them  accordingly. 


EXERCISES.  481 

(e)  You  say  it  was  not  Homer  who  wrote  about  the  travels 
of  Odysseus.  What  of  it  ?  Somebody  must  have  known  about 
them,  and  what  difference  does  it  make  whether  we  call  him 
Homer  or  call  him  something  else  ? 

(/)  We  must  not  expect  too  much  happiness  in  this  world, 
for  the  Bible  warns  us  that  "  man  is  born  unto  trouble,  as  the 
sparks  fly  upward." 

7.  What  is  the  significance  of  the  statement  that  the  Iliad 
and  Odyssey  were  not  written  by  Homer,  but  by  another  man 
of  the  same  name?     What  would  be  the  significance  of  a  simi- 
lar statement  about  Moses  and  the  Pentateuch  ? 

8.  From  the  "Life  of  Professor  Huxley",  the  •"  Letters  of 
J.  R.  Green  ",  and  any  other  sources  of  information  that  you  can 
command,  find  out  exactly  what  it  was  that  Huxley  said  in  his 
retort  upon  the  Bishop  already  mentioned  on  page  n. 

9.  Estimate  the  following  arguments  : 

(a)  If  you  believe  in  the  survival   of   the  fittest,  you  must 
believe  that  this  old  manuscript  was  one  of  the  best  of  its  time, 
for  it  is  the  only  one  that  has  survived. 

(b)  This  book  is  authentic;  then  why  should  we  not  believe 
what  it  says? 

(<:)  This  text  of  Cicero  dates  from  the  twelfth  century  and 
that  only  dates  from  the  fourteenth,  then  why  isn't  this  a  bet- 
ter one  to  go  by  than  that  ? 

(d)  This  text  has  great  value  for  the  historian,  for  it  was 
restored  at  infinite  pains,  and  there  is  now  every  reason  to 
believe  that  it  is  substantially  correct. 

(e)  '  Come  and  have  your  fortune  told  by  Blank's  system  of 
palmistry.     No  man  of  science  has  ever  disputed  the  claims  of 
this  system.' 

10.  Herodotus  tells  of  certain  sailors  who  circumnavigated 
Africa  and  said  on   their  return  that  as  they  went  westward 
around  the  southern  extremity  of  the  land  the  sun  was  on  their 
right.      Herodotus  said  he  did  not  believe   this.      What  can 
we  infer  about   Herodotus,  and  what  can  we  infer  about  the 
alleged  voyage  ? 

11.  During   a  thunder-storm  the   cook   in   a  certain   house 
rushed  from  the  kitchen  exclaiming  that  she  had  seen  a  ball  of 
fire  enter  one  window  and  go  out  of  the  other.     What  probably 
were  the  facts  ? 

12.  Two  students  who  have  never  been  suspected  of  dis- 


482  EXERCISES. 

honesty  sit  near  each  other  at  an  examination  and  each  of  them 
writes  these  very  words :  "  Henry  George  was  the  great  orator 
of  the  Revolution;  it  was  he  who  said  in  Faneuil  Hall,  'Give 
me  liberty  or  give  me  life.' "  What  inference  can  be  drawn 
from  this  coincidence  ?  How  much  should  the  inference  be 
affected  by  the  protests  of  the  students  that  they  were  perfectly 
honest,  or  by  their  explanation  that  they  had  studied  together? 

13.  Estimate  the  value  of  the  following  arguments  : 

(a)  Vacillating  and  cruel  as  our  treatment  of  the  Indians  has 
often  been,  there  can  be  no  doubt  that  the  European  conquest 
of  America  has  been  a  good  thing  for  the  world.  Certain  it 
is  that  we  have  not  a  single  eminent  writer  of  history  who 
doubts  it. 

(d)  We  must  choose  between  A's  account  of  this  affair  and 
B's.  A's  has  never  been  seriously  disputed  ;  B's  has  been  dis- 
puted for  centuries.  How  then  can  we  hesitate  between  them  ? 

(c)  I  know  that  I  might  have  made  up  my  mind  to  act  other- 
wise ;  for  I  was  conscious  at  the  time  that  there  was  nothing  in 
me  to  prevent  it. 

(d)  The  great  influence  of  the  mind  over  the  body  is  well 
illustrated  by  such  facts  as  the  following :  People  often  dream 
that  they  are  falling  from  some  great  height,  and  if  the  dream 
stops  there  it  does  them  no  harm ;  but  if  any  one  dreams  that 
he  strikes  the  ground,  the  mental  shock   is  too  great,  and  it 
kills  him  instantly. 

14.  Pick  out  and  summarize  the  bare,  concrete,  observable 
facts   (real  or  imaginary)    stated  in  the  following  paragraphs  ; 
point  out  any  passages  in  which  matters  of  fact  and  matters  of 
opinion  are  confused  ;  assuming  the   concrete  facts  to   be  as 
stated,  show  what  they  prove ;  show  what  must  be  assumed  in 
order  that   the  conclusion  drawn  should  follow  from  the  con- 
crete facts ;  and  estimate  the  reasonableness  of  such  assump- 
tion or  assumptions. 

'  A  careful  observer  of  the  people  of  India  says :  More  sys- 
tematic, more  determined  liars  than  the  people  of  the  East 
cannot,  in  my  opinion,  be  found  in  the  world.  Yet,  strange  to 
say,  some  of  their  works  and  sayings  represent  a  falsehood  as 
almost  the  unpardonable  sin.  Take  the  following  example  : 
"The  sin  [of  killing  a  Brahman  is  as  great  as  that  of  killing  a 
hundred  cows  ;  and  the  sin  of  killing  a  hundred  cows  is  as 
great  as  that  of  killing  a  woman ;  and  the  sin  of  killing  a  hun- 


EXERCISES.  483 

dred  women  is  as  great  as  that  of  killing  a  child  in  the  womb; 
and  the  sin  of  killing  a  hundred  [children]  in  the  womb  is  as 
great  as  that  of  telling  a  lie."  ' 

'  The  duty  of  veracity  is  often  more  prominent  among  primi- 
tive peoples  than  among  the  more  civilized.  Among  those 
Hill  Tribes  of  India  which  have  been  most  secluded,  and  which 
have  retained  the  largest  measure  of  primitive  life  and  customs, 
fidelity  to  truth  in  speech  and  act  is  still  the  standard,  and  a 
lie  is  abhorrent  to  the  normal  instincts  of  the  race.  The 
Bheels,  a  race  of  unmitigated  savages,  are  yet  imbued  with  a 
sense  of  truth  and  honor  strangely  at  contrast  with  their  ex- 
ternal character.  The  Sowrahs  do  not  know  how  to  tell  a  lie. 
The  Arabs  are  more  truthful  in  their  primitive  state  than  when 
they  are  influenced  by  "  civilization  ".  The  word  of  a  Hottentot 
is  sacred.' 

'  It  is  found,  in  fact,  that  in  all  ages,  the  world  over,  primitive 
man's  highest  ideal  conception  of  deity  has  been  that  of  a  God 
who  could  not  tolerate  a  lie ;  and  his  loftiest  standard  of 
human  action  has  included  the  readiness  to  refuse  to  tell  a  lie 
under  any  inducement,  or  in  any  peril,  whether  it  be  to  a 
friend  or  to  an  enemy.  This  is  the  teaching  of  ethnic  concep- 
tions on  the  subject.  The  lie  would  seem  to  be  a  product  of 
civilization,  and  an  outgrowth  of  the  spirit  of  trade  and  barter, 
rather  than  a  natural  impulse  of  primitive  man.' 

'  It  would  seem  to  be  clear  that  the  best  moral  sense  of  man- 
kind everywhere  deems  a  lie  incompatible  with  the  idea  of  a 
holy  God,  and  consistent  only  with  the  spirit  of  man's  arch- 
enemy— the  embodiment  of  all  evil.'  (Condensed  from  Trum- 
bull :  "  A  Lie  Never  Justifiable.") 

15.  "You  say  that  development  drives  out  the  Creator;  but 
you  assert  that  God  made  you  :   and  yet  you  know  that  you 
yourself  were  originally  a  little  piece  of  matter,  no  bigger  than 
the   end  of  this  gold  pencil-case."     (Huxley.)     What  kind  of 
argument  is  this  ?     Estimate  its  force. 

1 6.  "  Nevertheless,  I  did   not  formerly  consider   sufficiently 
the    existence  of  structures  which,  as  far  as  we  can  at  present 
judge,  are  neither  beneficial  nor  injurious ;  and  this  I  believe 
to  be  one  of  the  greatest  oversights  as  yet  detected  in  my  work. 
I  may  be  permitted  to  say,  as  some  excuse,  that  I  had  two  dis- 
tinct objects  in  view  :  firstly,  to  show  that  species  had  not  been 
separately  created,  and,  secondly,  that  natural   selection    had 


484  EXERCISES. 

been  the  chief  agent  of  change,  though  largely  aided  by  the 
inherited  effects  of  habit,  and  slightly  by  the  direct  action  of 
the  surrounding  conditions.  I  was  not,  however,  able  to  annul 
the  influence  of  my  former  belief,  then  almost  universal,  that 
each  species  had  been  purposely  created ;  and  this  led  to  my 
tacit  assumption  that  every  detail  of  structure,  excepting 
rudiments,  was  of  some  special,  though  unrecognized,  service." 
(Darwin's  "  Descent  of  Man  ",  part  i.  chap.  2.)  What  tendency 
does  this  illustrate  ? 

17.  "The  assertion  of  a  fact  wholly  beyond  the  reach  of 
evidence,  for  or  against,  is  to  be  held  as  untrue."  (Bain's 
"  Logic  ",  p.  382.)  Discuss  this. 


APPENDIX 

(CONTAINING  A  BRIEF  A\'D  PURELY  FORMAL  TREATMENT  OF 
DEDUCTION,    WHICH    CAN    BE     USED    IN    CONNECTION 
WITH  CHAPTER  IV,  A  PART  OF  CHAPTER  V,  AND 
CHAPTERS    VHI-XVI;   OR    EVEN,   IN  CER- 
TAIN  CASES,   AS   A     SUBSTITUTE 
FOR  THEM.) 

LOGIC  deals  with  reasoning,  and  reasoning  when  put  into  words 
always  involves  statements  or  'Propositions'.  We  reason  correctly 
when  one  proposition  [p.  2]  or  set  of  propositions  warrants  another 
based  upon  it,  incorrectly  when  it  does  not.  [P.  6;  Chap.  X.] 

PROPOSITIONS  are  of  three  kinds:  Categorical,  where  the  state- 
ment contains  no  condition  or  alternative,  as  'It  is  raining';  Hypo- 
thetical, where  it  contains  a  condition,  as  'If  it  is  raining  the  grass 
is  wet';  Disjunctive,  where  it  contains  an  alternative,  as  'Either 
it  is  not  raining  or  the  grass  is  wet',  'A  is  either  B  or  C'  (=  Either 
A  is  B  or  A  is  C).  [P.  106.] 

Every  categorical  proposition  and  each  division  of  a  hypothetical 
or  disjunctive  contains  three  parts,  a  Subject  [pp.  3,  87],  a  Predicate, 
and  a  Copula  [Chaps.  VI,  VII;  p.  142]  between  them.  [Pp.  4,  5.] 
In  the  first  example  'It'  is  the  subject,  'raining'  the  predicate, 
and  'is'  the  copula.  The  copula  is  always  some  form  of  the  verb 
'to  be'  (with  or  without  a  'not').  There  are  propositions,  such 
as  'It  rains',  'John  who  is  the  son  of  Thomas  eats  apples',  which 
do  not  seem  to  contain  these  parts;  but  they  can  always  be  put 
into  regular  form:  'It  is  raining';  'John-who-is-the-son-of-Thomas 
is  a-person-who-eats-apples'.  [P.  132.] 

The  subject  and  the  predicate  of  a  proposition  are  called  Terms; 
and  no  matter  how  many  words  one  of  them  contains  it  is  only 
one  term. 

When  I  say  'Socrates  was  a  man'  I  mean  two  things:  first, 
that  he  was  one  of  the  large  class  or  group  of  individuals  that  we 
call  men;  second,  that  he  had  certain  attributes,  such  as  reason, 

485 


486  APPENDIX. 

two  legs  instead  of  four,  etc.  When  my  thought  is  concerned  mainly 
with  the  first  of  these  two  meanings  the  word  'man'  is  said  to  be 
used  'Denotatively',  or  in  its  'Extension';  when  my  thought  is  con- 
cerned mainly  with  the  second,  the  term  is  used  'Connotatively' 
or  in  its  '  Intension '.  Thus  "the  Denotation  of  a  term  consists  of 
the  things  to  which  it  applies,  the  Connotation  consists  of  the  prop- 
erties which  it  implies."  [P.  58.] 

Proper  names,  like  'Socrates'  in  the  above  example,  have  exten- 
sion but  no  intension;  for  if  they  have  a  meaning  it  has  little  or 
nothing  to  do  with  t'.ieir  use.  Abstract  nouns,  on  the  other  hand, 
such  as  '  pride  '  or  'goodness',  have  intension,  but  no  extension; 
for  they  are  intended  to  abstract  or  draw  away  our  thought  from 
things  and  keep  it  fixed  on  properties  pure  and  simple. 

Terms  which  have  both  denotation  and  connotation — both 
extension  and  intension — are  called  Connotative;  those  which 
have  one  but  not  the  other  are  called  Non-Connotative.  Proper 
names  and  Abstract  terms  are  therefore  both  non-connotative. 
Adjectives  as  well  as  common  nouns  are  connotative.  [P.  60.] 

In  logic  it  is  generally  more  convenient  to  deal  with  the  extension 
of  terms  than  with  their  intension,  and  consequently  in  this  appendix 
terms  will  generally  be  interpreted  in  this  way  even  though  it  in- 
volves some  distortion  of  the  meaning. 

The  terms  'Athenian',  'man',  'animal',  all  have  both  extension 
and  intension;  but  they  do  not  have  the  same  amount  of  each. 
To  be  a  man  one  must  be  alive  and  able  to  move  about  like  any 
other  animal  and  also  have  the  peculiar  properties  of  humanity, 
such  as  two  legs  and  the  power  of  reasoning;  to  be  an  Athenian 
one  must  have  all  the  properties  of  a  man  and  also  be  born  or  live 
in  Athens.  Hence  the  word  'man'  has  more  Intension  than 
'animal',  and  'Athenian'  more  than  'man'.  But  with  the  Exten- 
sion of  the  terms  these  relations  are  reversed.  The  class  'Athe- 
nians' contains  fewer  individuals  than  the  class  'men',  and  the  class 
'men'  fewer  than  the  class  'animals'.  Hence  the  general  rule 
that  as  you  increase  the  Intension  of  a  term  you  tend  to  decrease 
its  Plxtension,  and  vice  versa. 

This  principle  of  inverse  relation  between  extension  and  intension 
is  made  use  of  in  DEFINITION.  When  1  define  'man'  as  'a  rational 
animal'  I  assume  that  the  class  'animal'  is  larger  than  the  class 
'man'  and  that  the  word  'rational'  shows  exactly  where  the  line 


APPENDIX.  487 

should  be  drawn  between  men  and  other  animals;  and  when  I 
define  'Athenian'  as  'a  man  born  in  Athens'  I  assume  still  another 
line  to  be  drawn  so  as  to  include  a  still  smaller  group.  In  each 
case  the  individuals  included  by  the  subject  of  the  definition  are 
exactly  the  same  as  those  included  by  the  predicate.  If  the  defini- 
tion is  correct  all  Athenians  are  men  born  in  Athens  and  all  men 
born  in  Athens  are  Athenians.  Thus  in  Definition  we  always 
state  the  intension  of  a  term  so  as  to  give  it  the  proper  extension, 
and  the  best  way  to  test  a  definition  is  to  find  out  whether  it  includes 
anything  that  the  term  does  not  really  stand  for  or  excludes  any- 
thing that  it  does. 

There  are  five  formal  rules  for  definitions: 

1.  The  subject  and  predicate  of  a  definition  must  have  exactly 
the  same  extension. 

2.  A  definition  should  state  the  essential  attributes  of  the  class 
defined.     We  should  not  define  'man'  as  'the  animal  that  cooks  his 
food'    even   though   all   men  might   be   distinguished   from   other 
animals  in  this  way;  for  we  know  of  other  distinctly  human  charac- 
teristics that  are  more  nearly  fundamental. 

3.  A  definition  must  not  contain  the  name  defined.     If  it  does 
there  is  said  to  be  Circulus  in  Definiendo. 

4.  The  defining  words  must  not  be  obscure,  figurative  or  ambig- 
uous.    It  is  useless  to  define  'ignotum  per  ignotius'. 

5.  A  definition  should  not  be  negative  where  it  can  be  affirmative. 
It  is  better  to  tell  what  a  term  means  than  what  it  does  not  mean. 
[Pp.  30.  ff.] 

When  we  analyze  a  group  of  objects  into  a  set  of  smaller  groups 
we  are  said  to  DIVIDE  it.  Thus  we  can  divide  all  living  things 
into  plants,  animals  and  protista,  or,  if  we  like,  into  pine-trees  and 
living  things  that  are  not  pine-trees.  Every  definition  implies 
division;  for  when  we  define  man  as  a  rational  animal  we  imply 
that  there  are  two  kinds  of  animals,  the  rational  and  the  non- 
rational. 

Any  group  divided  into  others  is  called  (in  logic)  a  Genus,  and 
each  one  of  the  smaller  groups  a  Species.  'Man'  is  a  species  with 
reference  to  'animal',  a  genus  with  reference  to  'Athenian'.  When 
there  are  divisions  and  sub-divisions  the  highest  group  of  all — that 
which  contains  all  the  species  and  sub-species — is  called  the  Sum- 
mum  Genus,  and  each  one  of  the  lowest  is  called  an  Infima  Species. 


488  APPENDIX. 

The  respect  (such  as  color,  shape,  nationality)  with  reference  to 
which  we  divide  objects  is  called  the  Fundamentum  Divisionis. 
The  attributes  by  which  a  species  is  distinguished  from  other  species 
of  the  same  genus  are  Differentia.  Qualities  peculiar  to  a  species 
but  not  used  to  define  it  or  distinguish  it  from  other  species  are 
Propria  or  Properties.  Qualities  or  states  which  are  present  but 
not  characteristic  of  a  species  are  Accidents.  A  thing  so  peculiar 
that  it  cannot  be  brought  into  the  same  class  with  others  (such 
as  the  rings  of  Saturn)  is  Sui  Generis. 

Division  into  two  species  according  as  objects  have  or  have 
not  a  given  quality  is  Division  by  Dichotomy. 

It  is  evident  that  the  extension  of  a  genus  is  greater  and  the 
intension  less  than  that  of  one  of  its  species. 

There  are  four  rules  for  correct  division: 

1)  The  species,  of  any  one  genus  must  not  overlap. 

2)  Taken    together  they  must  contain  exactly  the  same  objects 
as  the  genus,  i.e.,  have  the  same  extension. 

3)  They   should   be   distinguished   with   reference   to   the   same 
Fundamentum  Divisionis. 

4)  Divisio  non  facial  saltum,  i.e.,  it  should  be  carried  out  step 
by  step,  not  by  leaps.     [Chap.  IV.] 

In  Division  and  Definition  we  give  some  account  of  all  the  members 
of  a  group;  but  in  ordinary  propositions  we  often  do  not.  When  I 
say  'All  cows  like  hay'  I  ami  talking  about  all  the  members  of  the 
class  'cow',  but  presumably  only  about  part  of  the  class  '  creatures 
that  like  hay,'  namely,  the  cow  part;  and  when  I  say  'Some  cows 
like  hay'  I  do  not  speak  about  all  the  members  of  either  of  these 
classes. 

When  it  is  clear  that  a  term  refers  to  all  the  members  of  a  class 
it  is  said  to  be  Distributed;  otherwise  it  is  Undistributed.  [P.  135.] 

Propositions  are  divided  according  to  the  distribution  of  their 
subjects  into  two  classes:  Univcrsals,  which  distribute  their  sub- 
jects, e.g.,  'All  A  is  B',  'No  A  is  B';  and  Particulars,  which  do 
not,  e.g.,  'Some  A  is  B',  'Some  A  isn't  B'.  Their  determination 
in  this  respect  is  their  Quantity.  They  are  also  divided  according 
to  Quality  into  Affirmative  and  Negative. 

Taking  Quantity  and  Quality  together  we  get  four  kinds  of 
proposition,  each  represented  by  one  of  the  vowels  in  'Affirmo'  and 
'Nego': 


APPENDIX.  489 

A,  Universal  Affirmative,  as  'All  S's  are  P's'. 

E,  Negative,  as  'No  S's  are  P's'. 

I,    Particular  Affirmative,  as  'Some  S's  are  P's'. 

O,         "         Negative,  as  'Some  S's  are  not  P's'. 

Singular  propositions,  which  tell  about  ?ome  one  definite  indi- 
vidual (e.g.,  My  right  hand  is  sore,  John  Smith  is  dead),  can  gener- 
ally be  treated  as  universals.  They  tell  about  all  the  objects  in  a 
class  of  one. 

Propositions  whose  quantity  is  not  indicated  (such  as  'Boys  will 
be  boys';  cannot  be  used  in  formal  logic  until  it  is.  [Chap.  VIII.] 

Of  these  four  propositions,  A  and  O  are  said  to  be  contradictory 
to  each  other,  for  whenever  one  is  false  the  other  is  true,  and  vice 
•versa.  E  and  I  are  also  Contradictories.  A  and  E  are  Contraries, 
but  not  Contradictories,  for  while  both  cannot  be  true,  both 
may  be  false.  To  refute  either  of  them  it  is  sufficient  to  prove  the 
particular  proposition  of  opposite  quality. 

The  truth  of  a  universal  proposition  involves  the  truth  of  the 
particular  proposition  of  the  same  quality — i.e.,  of  the  '  Subalternate ' 
— and  the  falsity  of  the  particular  involves  the  falsity  of  the  universal 
(the  'Subalternans'). 

The  mutual  implications  of  these  four  propositions  are  known 
as  their  OPPOSITIONS.  For  two  propositions  to  be  'opposed'  in 
this  sense  it  is  not  necessary  that  there  should  be  any  inconsistency 
between  them.  [Chap.  IX.] 

Propositions  E  and  I  tell  exactly  as  much  about  the  things  named 
in  the  predicate  as  about  those  named  in  the  subject.  If  'No  men 
are  horses'  (E)  the  two  classes  lie  entirely  outside  of  each  other 
(see  diagrams,  p.  141)— the  predicate  as  well  as  the  subject  is 
distributed — and  it  is  equally  true  that  'No  horses  are  men'  (E). 
If  'Some  men  are  mortal'  (I)  the  classes  overlap  and  it  follows 
that  at  least  'Some  mortals  are  men'  (I).  In  this  case  neither 
subject  nor  predicate  was  distributed. 

Transposing  the  subject  and  predicate  in  this  way  is  called 
CONVERSION  [Chap.  XI];  and  in  the  cases  just  given  the  con- 
version was  'Simple' — the  quantity  of  the  proposition  remained 
unchanged. 

With  proposition  A  simple  conversion  would  be  illogical.  When 
we  say  'All  men  are  mortal'  the  subject  is  distributed,  but  not  the 
predicate — there  may  or  may  not  be  mortals  who  are  not  men; — 


490  APPENDIX. 

and  so  in  converting  we  can  only  say  that  at  least  some  mortals 
are  men.  Thus  the  converse  of  A  is  I.  It  does  not  give  so  much 
information  as  the  original  proposition,  for  we  could  not  convert 
back  again  to  A,  but  only  to  I.  Conversion  from  A  to  I  is  said  to 
be  per  accidens  or  by  limitation. 

Proposition  O  cannot  be  converted  at  all.  Like  E  it  distributes 
its  predicate.  But  it  does  not  tell  much  about  it.  If  some  birds 
are  not  green  it  is  certain  that  no  green  thing  is  one  of  those  birds. 
Yet,  for  all  that  we  have  been  told,  every  green  thing  may  be  a 
bird  nevertheless. 

For  correct  conversion  remember  two  things:  that  universal 
propositions  distribute  their  subjects;  negative  propositions,  their 
predicates; — and  that  when  we  convert  them  no  term  may  be  dis- 
tributed in  the  Converse  which  was  not  already  distributed  in  the 
Convertend. 

Remember  also  that  the  common  form  of  words  'All  S  is  not  P' 
is  ambiguous  and  misleading.  It  may  mean  'No  S  is  P',  i.e.* 
'There  is  not  any  S  which  is  P'  (E).  Or  it  may  mean  'It  is  not 
true  that  all  S  is  P',  i.e.,  'At  least  some  S  is  not  P'  (O).  Logicians 
agree  to  take  it  in  the  latter  sense.  [P.  98.] 

Exclusive  propositions,  such  as  'Only  the  brave  deserve  the  fair', 
'Yours  alone  escaped',  distribute  their  predicates  and  can  be  con- 
verted accordingly,  e.g.,  All  who  deserve  the  fair  are  brave,  All 
that  escaped  are  yours.  (For  the  distinction  between  Exclusive 
and  Exceptive  propositions  see  p.  103  ) 

To  OBVERT  [p.  130]  a  proposition  is  to  change  an  affirmative 
into  a  negative  with  the  same  meaning,  or  vice  versa;  e.g.,  'All 
men  are  mortal'  into  'Xo  men  are  immortal',  etc.  It  is  simply 
a  matter  of  changing  both  the  copula  and  the  predicate.  The  sub- 
ject and  the  quantity  of  the  proposition  remain  the  same. 

By  combining  Obversion  and  Conversion  we  can  get  some  rather 
curious  results  (see  p.  138),  of  which  two  should  be  remembered. 
The  first  of  these  is  a  kind  of  converse  for  O.  'Some  boys  arc 
not  good'='Some  boys  are  bad'='Some  bad  people  are  boys'. 
The  other  is  an  inference  from  A.  'All  men  are  mortal '=  'Xo  men 
are  immortal^ 'Xo  immortals  are  men' = 'All  immortals  are 
non-men'.  Thus  from  'All  S  is  P'  we  get  'Xo  non-P  is  S'  and 
'All  non-P  is  non-S '.  But  we  do  not  get  'All  non-S  is  non-P'. 

In  Conversion  and  Obversion  the  inference  is  said  to  be  immediate 


APPENDIX.  491 

[Chap.  XI];  we  go  directly  to  the  conclusion  from  a  single  premise. 
In  SYLLOGISM  [Chaps.  XII-XVII]  the  inference  is  mediate  [Chap. 
XII],  i.e.,  the  conclusion  is  drawn  by  means  of  a  Middle  Term  con- 
tained in  each  of  two  premises,  e.g.,  'All  men  are  mortal,  All  Greeks 
are  men,  .'.  All  Greeks  are  mortal'. 

This  example  is  of  a  Categorical  Syllogism,  for  each  of  the 
premises  is  a  categorical  proposition. 

To  have  even  the  outward  form  of  a  Categorical  Syllogism  there 
must  be  exactly  three  propositions  (two  premises  and  a  conclusion) 
and  exactly  three  terms,  each  one  occurring  in  two  different  proposi- 
tions. The  'Middle'  term  occurs  in  each  of  the  premises  but 
not  in  the  conclusion.  The  predicate  of  the  conclusion  is  always 
the  'Major'  term,  and  the  subject  of  the  conclusion  the  'Minor'. 
(I"  all  Greeks  are  mortal  the  class  'mortals'  is  as  big  or  bigger  than 
the  class  'Greeks'.)  The  premise  which  contains  the  major  term 
is  the  Major  Premise;  that  which  contains  the  minor  term,  the 
Minor  Premise.  In  very  formal  arguments  the  ma;or  premise 
is  put  first,  the  minor  second,  and  the  conclusion  last;  but  we 
cannot  depend  on  this  when  we  have  to  pick  them  out.  Sometimes 
one  of  the  three  is  not  even  stated. 

The  rules  for  correct  syllogistic  reasoning  should  be  both  under- 
stood and  remembered.  They  are  given  on  the  bottom  of  p.  177. 

The  'Fallacies'  or  blunders  in  reasoning  which  we  are  most 
likely  to  make  with  syllogisms  are  four,  to  wit: 

1.  Ambiguous   Middle,    e.g.,    Charles    is    King,    and    'King'    is 
four  letters,  .'.  Charles  is  four  letters.     Here  there  are  really  four 
terms:    'Charles',  'four  letters',  'King'  the  name  of  a  word,  and 
'King'  the  name  of  a  ruler.     [P.  22  ff.] 

2.  Undistributed  Middle,  e.g.,  All  A  is  B,  All  C  is  B,  .'.  All  A 
is  C.     This  is  like  saying  that  all  cows  are  horses  because  they  are 
both  creatures  that  eat  hay.     [Pp.  158  n.,  166  n.,  175  n.] 

3.  Illicit  Major,  where  the  major  term  is  distributed  in  the  con- 
clusion but  not  in  the  premise,  e.g.,  All  S  is  M,  Some  P  is  not  M,  .'. 
Some  S  is  not  P.     [Pp.  158  n.,  170  n.,  174  n.]     This  is  like  saying 
all  crows  are  black,  Some  birds  are  not  black,  .'.  Some  crows  are 
not  birds. 

4.  Illicit  Minor,  e.g.,  All  M  is  S,  All  P  is  M,  .'.  All  S  is  P;   All 
children  are  human,  All  human  beings  are  mortal,  .'.  All  mortals 
are  children.     [Pp.  158  n.,  170  n.,  174  n.] 


4Q2  APPENDIX. 

These  fallacies  can  all  be  detected  by  diagrams  if  we  put  one 
circle  (or  part  of  a  circle)  within  another  when  one  class  (or  part 
of  a  class)  is  said  to  be  part  of  another,  and  then  see  whether  the 
state  of  affairs  asserted  in  the  conclusion  is  necessarily  represented. 
(See  pp.  141,  161,  174,  177.) 

In  the  last  example  we  had  no  right  to  conclude  that  all  mortals 
are  children, — all  S  is  P;  but  we  might  have  concluded  that  all 
children  are  mortal, — all  P  is  S.  This  shows  that  we  have  to  pay 
strict  attention  to  the  order  of  our  terms;  for,  as  we  have  seen,  the 
subject  and  predicate  do  not  always  have  the  same  quantity. 

As  the  terms  in  a  syllogism  can  be  arranged  in  four  different 
ways,  there  are  four  different  'FIGURES'  of  the  Syllogism  [p.  148; 
Chaps.  XIII-XVI]  as  follows — S  standing  for  the  Minor  term  (the 
Subject  of  the  conclusion);  P  for  the  Major  (the  Predicate  of  the 
conclusion);  and  M  for  the  Middle: 

I.  II.  III.  IV. 

Major MP          PM          MP          PM 

Minor SM          SM          MS          .AS 

Conclusion SP  SP  SP  SP 

Since  each  one  of  the  three  propositions  in  a  figure  may  be  either 
A,  E,  I  or  O,  each  figure  contains  64  possible  Moods  or  kinds  and 
arrangements  of  propositions, — A  A  A,  A  A  E,  A  A  I,  A  A  O, 
A  E  A,  etc. 

Of  course  the  moods  are  not  all  valid.  Many  of  them  break  some 
rule  of  the  syllogism  in  any  figure,  e.g.,  I  O  A  (i.e.,  major  premise  I, 
minor  O,  and  conclusion  A),  which  not  only  has  two  particular 
premises  but  also  has  an  affirmative  conclusion  with  a  negative 
premise.  Others  break  a  rule  in  one  figure,  but  not  in  another. 

To  remember  the  valid  syllogisms  logicians  invented  at  least 
six  hundred  years  ago  some  curious  hexameters,  as  follows: 

Barbara,  Celarent,  Darii,  Ferioque,  prioris; 
Cesare,  Camest-res,  Festino,  Baroko,  secundse; 
Tertia,  Darapti,  Disamis,  Datisi,  Felapton, 
Bokardo,  Ferison,  habet.    Quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Frcsison. 

The  vowels  in  the  italicized  words  show  the  moods,  and  the  real 
Latin  words  show  the  figures  in  which  they  are  valid.  'Barbara'  is 


APPENDIX.  493 

therefore  the  name  of  the  valid  syllogism  A  A  A  in  the  first  figure; 
'Cesare'  of  E  A  E  in  the  second.  The  initial  letters  show  what  syl- 
logism in  the  first  figure  the  others  can  be  '  reduced '  to  [p.  1 78], 
and  some  of  the  other  consonants  show  how  the  reduction  is  made. 
These  lines  have  a  certain  historic  value,  but  nowadays  hardly 
any  one  uses  them;  though  we  do  occasionally  see  the  word  Bar- 
bara, and  a  few  of  the  others. 

For  other  deductive  arguments,  see  Chapter  XVII. 

For  semi-logical  and  material  fallacies,  see  the  text  as  follows: 

Equivocation,  Chap.  II,  pp.   13  ff. 

Amphibology,  Accent  and  Accident,  Chap.  Ill,  pp.  39  ff. 

Composition  and  Division,  Chap.  V,  p.  64. 

Non  Sequitur,  Chap.  XVIII,  p.  195. 

Petitio  Principii  and  Ignoratio  Elenchi,  Chap.  XIX,  pp.  196  ff. 

Many  Questions,  Chap.  XX,  p.  207. 

Post  Iwc,  ergo  propter  hoc,  Chap.  XXVI,  p.  272. 


INDEX. 


Abstract  nouns,  60  ;  definition  of, 

67. 

Abstractions,  hypostatising,  66. 
Abstractly  denominated  principle, 

fallacy  of,  369. 
Absurd  questions,  208. 
Absurdity  as  test  of  truth,  414. 
Accent,  fallacy  of,  39,  43. 
Accident,  fallacy  of,  42,  43. 
Accidents,  definition  of,  50. 
Accuracy,  misplaced,  306. 
Agreement,  double  method  of,  277; 

method  of,  261  ff. 
Ambiguities,  13  ff. ;  of  quality  and 

quantity,  98. 
Amphibology,  39,  42  n. 
Analogy,     argument   from,      413  ; 

false,  209. 
Analysis,  causal,  257;  hexateuchal, 

379- 

Analytic  propositions,  82. 
Antecedent,     106,     270 ;    denying 

the,  185. 

Appeal  to  consequences,  10. 
Apperception,  412  n. 
Apprehension,  simple,  5  n. 
Aquinas,  Thos.,  107. 
Archimedes,  326. 
Areolus,  Petrus,  41 7  n. 
'  Argument ',  legal.  40x3  n. 
Arguments,  abbreviated,  188. 
Argumentum  ad  hominem,  12,  201, 

202  ;  ad  populum,  12,  201,  202; 

ad  rem,  12;  ad  verecundiam,  367. 
Aristotle,  4on.,  8311.,  133  n.,  176, 

214,  420. 

Arnold,  Matthew,  42. 
Authority,  argument  from,  367. 
Authorship,  joint,  378. 
Averages,  general,  312. 


Bacon,   Francis,    23,   249,   262 n.; 

Roger,  262  n. 
Bailey,  68  n. 
Bain,  68  n. 

Berkeley,  15  n.,  68  n.,  36811. 
Bismarck,  199. 
Boole,  107. 
Bosanquet,  61. 
Bowditch,  320  n. 
Bradley,  107. 
'Bulls ',  210. 
Burnham,   W.  H.,   350 n.,  35 in., 

354  n. 

Canning,  200. 

Causal  analysis,  257. 

Causal  interaction,  245. 

Causation,  235  ;  peculiarities  of, 
247. 

Cause,  238;  false,  fallacy  of,  272. 

Causes,  combined,  283  ff. ;  com- 
plex, 281;  compounded,  283  ff.; 
counteracting,  281;  plurality  of, 
267,  282;  quantitative  treatment 
of,  287;  vicariousness  of,  267. 

Categories,  77,  83. 

Characteristic  imperfection,  268. 

Chance,  332  n. 

Change,  84. 

Circulus  in  probando,  198. 

Circumstances,  233  ff. 

Classification,  50,  162. 

Composition,  fallacy  of,  39  n.,  64, 

211. 

Comstock,  329. 

Conceivability  as  test  of  truth,  405, 

406,  421. 

Conclusion  defined,  121. 
Concomitant  variations,  method  of, 

290,  296. 

495 


496 


INDEX. 


Confirmation  of  statements,  393. 
Connotation,  60  n. 
Consequences,  appeal  to.  10. 
Consequent,    1 06,    270 ;    affirming 

the,  185. 

Consistency,  124,  392,  405,  421. 
Contradiction,     law    of,     126  ;    of 

statements,  393. 
Contrary  propositions,  73. 
Conversion,  13 1 ;  by  negation,  138 ; 

per  accidens,  136. 
Copula.  128  n.,  143. 
Correlative  terms,  74. 
Coulanges,  Fustel  de,  i6n. 
Credulity,  345. 
Cross-division,  47. 
Cross-references,  49. 

Davis,  2OI  n. 

Deduction,     122  ;    limitations    of, 

145,  221. 
Definition,   30,   241 ;  and  division, 

45  ;  how   to   find,    30  ;  how    to 

frame,  31;  illustration  in,  32;  of 

things,  34. 
De  Morgan,  72. 
Demurrer,  400  n. 
Denotation,  61. 
Descartes,  243,  420,  423. 
Difference,  indirect  method  of,  278; 

methods  of,  261,  262,  288. 
Differentiae,  32,  50. 
Dilemmas,  186. 
Distributed  term,  135. 
Division,  and  classification,  45 ;  by 

dichotomy,  46  ;  fallacy  of,    64; 

relation  to  definition,  45. 
Donation  of  Constantine,  377. 

Elimination,  method  of,  254. 

Enthymeme,  188. 

Epicheirema,  188,  189. 

Episyllogism,  189. 

Epithets,  question-begging,  63. 

Error,  measures  of,  327. 

Euler's  diagrams,  I2on.,  140  ff, 
177. 

Everett,  C.  C-,  I3°n- 

Evidence,  circumstantial,  361 ;  ex- 
pert, 367  ff. ;  issue  before,  402. 

Exaggeration,  38. 

Excluded  middle,  law  of,  128. 


Exhaustion,  method  of,  250,  265.* 
Existence,  denials  of,  89. 
'  Expectation  of  life',  326. 
Experiment,  272  ff. 
Explicative  propositions,  82. 
Extension,  61. 

Fact  and  feeling,  10. 

Faith,  425. 

Fallacies,  classification  of,  191; 
jingle,  194;  of  forgotten  issue, 
195  ff.;  of  ill-conceived  universe, 
195;  'purely  logical',  193;  re- 
flex, 194.  _ 

Feeling  and  judgments,  II. 

Forgotten  issue,  fallacy  of,  195  ff. 

Forgotten  man,  the,  216. 

Fowler,  I97n.,  223  n.,  277. 

Fundamenta  divisionis,  48,  53. 

Galen,  176. 
Galton,  316. 
Genung,  210. 
Genus,  32,  49. 
Geometry,  248,  406. 
Grand  Remonstrance,  36. 
Greenleaf,  44  n.,  385^ 
Group  comparisons,  296. 
Guessing  in  induction,  252. 

Hamilton,  SirWm.,  107,  136. 

Hay,  John,  350. 

Hearsay,  384. 

Hegel,  19,  368. 

Herschel,  261. 

History,  356;  limits  of,  358  ;  mon- 

uments  in,  359. 
Hodge,  A.  A.,  25  n. 
Hodge,  C.  F.,  370. 
Hodgkin,  Thos.,  377  n. 
Honesty,  intellectual,  10. 
Hume,    4,  5,   15  n.,  83  n.,  262  n., 

33*  n- 

Huxley,  10,  239. 
'  Hypotheses  non  fingo',  4T9- 
Hyslop,  75. 

Ideas,  4;  classification  of,  52. 
Identity,  individual,  78,  162,  254 ; 

and  similarity,  81;  peculiarities 

of,  245;  law  of,  125. 
Ignoratio  elenchi,  198. 


INDEX. 


497 


Illicit  major,  158  n.,  170,  174  n. 

Illicit  minor,  158  n.,  17011.,  174.11. 

Illusion,  91. 

Inductio  per  enumerationem  sim- 
plicem,  251,  257. 

Induction,  122;  Aristotelian,  250  ; 
certainty  of,  226;  distinguished 
from  deduction,  22 1  ;  perfect, 
227,  250. 

Inference,  121;  by  added  deter- 
minants, 75  ;  by  privitive  con- 
ception, 130;  data  for,  270;  im- 
mediate, 131;  in  observation, 
343;  mediate,  145;  real,  152. 

Infima  species,  50. 

Infinitation,  130. 

Innate  principles,  230. 

Intension,  61. 

Interaction,  235;  causal,  245. 

Interest,  errors  due  to,  302. 

Interpretation,  blunders  of,  13. 

Irrelevance,  198. 

Jevons,  4,  5n.,  16,  42  n.,  5On., 
64  n.,  70  n.,  75,  103  n.,  107, 
107  n.,  137,  186,  214,  251  n., 
320n.,  324 n.,  325,329. 

Johnson,  Sam.,  31. 

Judgment,  2. 

Kant,  15  n.,  83  n.,  107,  368,  422. 
Keynes,   83  n.,  87,  87 n.,  88,  107, 

rogn.,  H5n.,   n6n. 
Kidd,  Benjamin,  370. 
Kipling,  R.,  93. 
Knowledge,  4,  425. 

Law,  notion  of,  237,  244. 
Langlois-Seignobos,    15  n.,    37  n., 

68,  69. 

Leibnitz,  206,  417. 
Lies,  honest,  352. 
Locke,  4,  15  n.,  4on.,  61,  62,  206, 

398. 

Logic,  definition  of,  6;  scope  of,  6. 
Lotze,  68n.,84n.,  106  n.,  215. 
Lyell,  411. 

Mai -observation.  348. 
Manning,  Cardinal,  370. 
Mansel,  107. 
Many  questions,  fallacy  of,  207. 


Martensen,  25  n. 
Martineau,  Jas.,  66  n.,  68  n. 
Mean,  arithmetical,  313  ;  general, 
312;  geometrical,    313;     kinds, 

of,  3*3- 

Means  and  end,  84. 

Median,  316. 

Memory,  343. 

Mercier,  208. 

Merriman,  329. 

Method,  indirect,  of  difference,  278; 
joint,  275;  of  agreement,  264; 
of  concomitant  variations,  290, 
296;  of  difference,  261,  288;  of 
elimination,  254;  of  exhaustion, 
250;  of  residues,  288  ;  of  statis- 
tics, 296. 

Methods,  the  four,  262. 

Mill,  J.  S.,  35,  83  n.,  107,  261, 
262,  263,  278,  284,  287,  290  n., 
292,  295  n. 

Minto,  2on.,  48 n.,  64  n.,  83  n., 
looff.,  104  n.,  i86n.,  210  n., 
251  n.,  262  n.,  349  n.,  369,  370. 

Modus  ponens,  183. 

Modus  tollens,  183. 

Motet,   353. 

Naming,  use  of,  55. 

Neglected  articulation,  212  ;  as- 
pect, 211;  member,  215;  whole, 
219. 

Newton,  I.,  244,  419 

Nicolay,  Col.,  350. 

Noetic  relation,  82. 

Non -observation,  348. 

Non-sequitur,  195. 

Nouns,  common,  60. 

Number,  85. 

Object  of  thought,  3. 
Objections,  fallacy  of,  220. 
Observation,    343  ;    unprejudiced, 

347- 

Obversion,  130. 
Occam's  razor,  417. 
Opposite  term%  73. 

Parsimony,  law  of,  418. 
Permutation,  130. 
Personal  equation,  300 
Petitio  principii,  196. 


498 


INDEX. 


Phrases,  conventional,  36 ;  uses 
of,  56. 

Plato,  133  n. 

Pleadings,  400. 

Post  hoc,  ergo  propter  hoc,  272 

Powell,  Baden,  223  n. 

Precision,  where  needed,  34. 

Preconception,  errors  of,  302. 

Predicate,  quantification  of,  136. 

Premise,  121  ;  major,  150,  169; 
minor,  150. 

Probability,  330  ff. ;  as  a  test  of 
truth,  392;  value  of  finding,  334. 

Probable  error,  328. 

Proof,  limits  of,  423. 

Proper  nouns,  60. 

Prophecy,  356. 

Propositions,  2,  82;  accidental,  82 ; 
affirmative,  96;  ampliative,  82; 
analytic,  82  ;  categorical,  106; 
contradictory,  113,  114,  117; 
contrary,  113,  114,  117;  copu- 
lative, io6n.  ;  disjunctive,  106  ; 
essential,  82  ;  exceptive,  103, 
115;  exclusive,  103,  115;  expli- 
cative, 82  ;  formal  characteris- 
tics of,  96  ;  hypothetical,  106; 
indefinite,  99  ;  indesignate,  99; 
modal,  85,  86 ;  negative,  96, 
io6n. ;  opposition  of,  in;  par- 
ticular, 96,  lion.;  preindesig- 
nate,  99  ;  pure,  85  ;  real,  82 ; 
remotive,  106  n. ;  singular,  96, 
H3n.  ;  subaltern,  114;  subal- 
ternate,  114;  subcontrary,  114; 
synthetic,  82;  universal,  96,  109; 
verbal,  82. 

Propria,  50. 

Prosyllogism,  189. 

Quality,  96;  undesignated,  99. 
Quantity,  96,  97;  double,  102;  un- 
designated, 99. 

Reality,  conception  of,  91. 
Reasoning,  correct,  6;  to  the  point, 

12. 

Reduction  of  oblique  figures,  178. 
References,  fallacy  of,  369. 
Relations,    combined,    84;  denials 

of,    89  ;  five    fundamental,     77; 

how  interwoven,  253. 


Residues,  method  of,  288. 

Schopenhauer,  76. 

Science,  and  religion,  425;  work 
of,  244. 

Selection,  accidental,  304. 

Sigwart,  79,  84. 

Simplicity  as  test  of  truth,  405, 
416,  421. 

Socrates,  241. 

Sorites,  188,  189. 

Space,  ideas  of,  5 ;  relation  of,  80. 

Species,  49. 

Spencer,  H.,  15  n.,  31,  89,  90. 

Statements,  interpretation  of,  36. 

Statistics,  method  of,  296. 

Stephen,  L.,  II. 

Subject,  and  attribute,  78;  of  re- 
lation, 87;  of  sentence,  3,  87; 
of  thought,  3. 

Sui  generis,  50. 

Suminum  genus,  50. 

Sumner,  W.  G.,  21  n.,  65  n.,  215  n., 
216. 

Syllogism,  145  ;  figures  of,  148; 
disjunctive,  186;  first  figure  of, 
150;  fourth  figure  of,  176;  hypo- 
thetical, 183;  rules  of,  177  n.; 
second  figure  of,  162  ;  third 
figure  of,  171. 

Synthetic  propositions,  82. 

Tenterden,  Lord,  43. 

Terms,  56;  absolute,  73;  abstract, 
65,  70;  collective,  63;  concrete, 
65;  connotative  and  non-conno- 
tative,  60  ;  contradictory,  73; 
contrary,  73;  contra  positive,  73; 
correlative,  74  ;  demonstrative, 
58,  69  n. ;  descriptive,  6911.; 
distributed,  135;  distributive,  63; 
general,  61;  negative,  71;  oppo- 
site, 73;  paronymous,  28;  posi- 
tive, 71,  75  ;  relative,  73,  74; 
singular,  61. 

Testimony,  363. 

Thinking,  clear,  2,  6 ;  clear  by 
analysis,  259  ;  hazy,  240;  logi- 
cal, 6  ;  objective,  6;  two  kinds 
of,  I. 

Thing,  233-4;  permanence  of, 
242. 


INDEX. 


499 


Thorndike,  Ashley,  378;  Edward, 
L.,  249  n. 

Thought,  blunders  in,  191;  laws 
of,  7,  121,  124;  objectof,  3;  sub- 
ject of,  3;  and  things,  9. 

Time,  ideas  of,  5 ;  relation  of,  80. 

Trumbull,  25  n. 

Truth,  double,  9  ;  impersonal,  7; 
tests  of,  405  ff. 

Truthfulness,  tests  of,  386  ff. 

Truths,  general,  254. 

Undistributed  middle,  158  n., 
i66n.,  175  n. 

Uniformity  of  Nature,  228,  232;  as 
test  of  truth,  405,  406,  421;  in 
the  mass,  409;  precision  in,  238; 
proof  of,  243. 

Universe,  assumed,  204;  ill-con- 
ceived, 195, 204 ;  of  discourse,  72. 


Universes,  confusion  of,  208. 

Variation,  average,  327. 

Venn,  J.,  53:1.,  55,  108,  312,  329, 

332 ,  340  n. 
Vera  causa,  420. 

Wallace,  A.  R.,  341,  341  n. 

Whately,  R.,  16,  3911.,  64n.,  107, 
197,  198,  199,  211,  212  n.,  21311., 
219,  220,  369. 

Whewell,  261. 

Whole  and  part,  84. 

Words,  ambiguous,  16,  22;  blun- 
ders in,  191;  categorematic,  58; 
meanings  of,  13;  oblique  senses, 
37  ff. ;  single,  uses  of,  56;  syn- 
categorematic,  58;  vague,  17, 
22. 


L  005  491    124  3 


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